
Class _ 1L. 

Book . , 
Copyright N°___ 

COPYRIGHT DEPOSIT. 



PRACTICAL 
COTTON CALCULATIONS 



A TREATISE RELATING TO 
COTTON YARN, CLOTH STRUCTURE, LOOM 
AND MISCELLANEOUS COTTON 
MILL CALCULATIONS , 



BY 

ERNEST WHITWORTB 

Formerly Principal ofth Designing and Cloth 

Analysis Department, New Bedford 

Textile School 



PUBLISHED B"i 

ERNEST WHITWORTB 

801 in BRIDGE, M \»>. 



LIBRARY of CONGRESS 
Two Cooies Received 

WAY 24 190f 

VU Copyright Entry 
CLASS Ou XXc., No. 
COPY B. 









Entered according to Acl of Congress in the year 1907 
by 

ERNEST WHITW< >RTH 

In the office < >f the Librarian of < longress 
Washington, I). C. 













PREFACE TO FIRST EDITION. 



There are several reasons why the author of 
this hook has deemed its publication advisable. 

One reason has been the apparent want of a 
book dealing only with practical calculations. 
This h;»s been borne in mind in the compilation 
of this hook. 

The principal objecl has been to pu1 into a 
convenient form for reference a text-book of 
practical cotton yarn, cloth and general mill 
calculations. 

Being the only hook on the market, so far as 
the author is aware, dealing only with practical 
cotton calculations, it is submitted to all persons, 
from student to superintendent, who have occa- 
sion to deal with cotton, mill calculations. 

.Most of the rules and methods explained in 
the following pages are deducted from data 
gathered from practical experience and have 
never been printed before. The remainder, with 
the exception of the yarn numbering and cloth 
production tables, are common property, and 
may be found in almost every book on textile 
calculations. These are principally length and 
weight calculations, where take-up or contraction 
is not considered. 



PREFACE TO SECOND EDITION. 



The favorable reception accorded the former 
issue of "Practical Cotton Calculations," and 
the many commendatory letters as to its value, 
received from practical cotton mill men, have 
indicated the advisability of issuing this edi- 
tion. 

On account of the growing, use of silk in the 
finer grades of fabrics composed for the greater 
part of cotton, data regarding raw silk calcula- 
tions have been here inserted. More extended 
references have also been made to fabrics com- 
posed of various colors; also to fabrics contain- 
ing more than one counts of yarn in both warp 
and filling. 

E. W. 

May, 1907. 



GLOSSARY OF TECHNICAL 
WORDS AND TERMS. 



In the cotton manufacturing business, va- 
rious words, forms and terms are used in differ- 
ed mills to indicate the same thing; for ex- 
ample, warp yarn is known by one or other of 
ih«' terms yarn, thread, end. twist, etc. For this 
reason it has been deemed advisable to define 
the following list of the principal words and 
terms which will be used throughout this book: 

Yarn. The final product of combined fibres 
after leaving the spinning frame or mule. 

Ply Yarn. Two or more single yarns folded 
or twisted together. 

Cord Yarn. A heavy ply yarn. 

Cabled Yarn. Two or more ply yarns twisted 
together. 

Picks. Pilling yarns. Each filling yarn 
laid ;it righl angles between the warp yarns is 
termed a pick. 

Sley. The number of cuds per inch in the 
cloth, provided each denl in the vrc(\ in which it 
w;is made contained an equal number of ends. 

Pick. The number of picks per inch in the 
cloth, provided slop or cheek pegs are not used. 

Average Sley. The average number of ends 
per Inch in the cloth when some dents contain 
more ends Hi, -in others. 



b PRACTICAL COTTON CALCULATIONS 

Average Pick. The average number of picks 
per inch in the cloth when check pegs are used. 

Count of Cloth. The sley and pick of a cloth. 

If a cloth is said to count 80X100, it means 
80 sley and 100 pick. The first number given 
always indicates the sley and the second num- 
ber the pick. 

A cloth is said to be square when the sley and 
pick are equal. 

Average Count of Cloth. The average sley 
and average pick of a cloth. 

When the average sley is different from the 
sley, or the average pick is different from the 
pick, the sley and pick, and average sley and 
average pick are usually written together, as 

follows : 

80 100 
110 124 

In some mills this means 80 sley X 100 pick 
for the ground of the cloth, and 110 sley X 124 
pick average, whereas in other mills the top line 
indicates the average and the lower the count of 
the base or ground of the cloth. The relative 
positions, above or below the line, of the ground 
and average count, are matters of choice. 

Counts or Numbers of Yarn. The relation- 
ship of length to weight in determining the size 
of yarn. Although the term "numbers" is 
used quite extensively the more universal term 
"counts" will be given preference in this book. 

Sley Reed. A reed that will produce a given 
sley in the cloth, provided two ends are drawn 
in each dent. 



PB ICTTCAL COTTON < \ i i i i \ nONS i 

Warp Pattern. One repeat of the arrange- 
menl of the differenl counts or differenl colors 
of llic warp yarns. 

Filling Pattern. One repeat of the differenl 
counts or differenl colors of the filling yams. 

The filling pattern may differ in extent Prom 
the pattern or effed shown on the face of the 
cloth. For example, the filling pattern in a 
Marseilles quill may repeat on a small number 
of picks, as six or eight, whereas live pattern 
formed by the weave would occupy an entire 
quilt. 

Selvedges or Selvages. Extra ends on the 
sides of the warp, used to strengthen the edges 
of the cloth and aid in keeping it at a uniform 
width. 

Fabric or Cloth. Warp and filling yarns 
combined and interlaced together. 

Multiplier. The oumber to multiply by. 

Product. The result of a multiplication 
problem. 

Sum. The result of an addition problem. 

Dividend. The number to be divided. 

Divisor. The number to divide by. 

Quotient. The resull of a division problem. 

Deduct. To subtrad or take Prom. 

-(- Pins or more, addition sign. 

X Multiplied by sign. 

-r- Divided by sign. 

— Minns or less, subtraction sign. 

R. P. M. Revolutions per minute. 



5 PRACTICAL COTTON CALCULATIONS 

CONSTANTS OR CONSTANT NUMBERS. 

In dealing with textile calculations there are 
several numbers that constantly occur, making 
it feasible in some cases to dispense with one or 
other by cancelling one into the other. 

The following list contains the principal con- 
stants that will lie used in this book: 
.12; 
8.33; 

.2314; 
4.32 in. or 4 5-16 in. ; 
764. 
The above constants, taken in rotation, are 
obtained as follows: 

.12 and 8.33. When 7000 (grains) and 840 
(yards) occur in the same calculation, the 7000 
may be dispensed with and .12 used instead of 
840, or the 840 may be dispensed with and 8.33 
used instead of 7000, 

because 840 -f- 7000 = .12, 
and 7000^ 840 = 8.33. 
In all calculations where a certain result may 
be obtained by multiplying by 8.33, the same 
result may be obtained by dividing by .12, or 
via vt zrsa, because 

1 X 8.33 = 8.33 
l-f-.12 =8.33 
( Mic yard of l's cotton yarn weighs 8^ grains. 
As most of the yarn calculations deal princi- 
pally with lengths and weights, the rules marked 
* will also apply to all other systems where 
higher counts indicate finer yarns by substituting 
their respective lengths instead of 840. 



PRACTICAL COTTON CALCULATIONS 9 

In calculations where the constant 8.33 ap- 
pears, the rules will apply to other materials by 
substituting the following numbers: Worsted, 
12.5; Woolen, run system, 4.375; Linen and 
Woolen, cut system, 23.33. The numbers given 
indicate the weight in grains of 1 yard of l's 
yarn in the respective materials. 

Instead of .12 the following numbers may be 
used : Worsted, .08 ; Woolen, run system, .228.+ ; 
Linen and Woolen, cut system, .043 — . 

If any rule marked * does not contain the 
number 840 or either of the constants .12 or 
8.33, it will apply just as it stands for other 
materials as well as cotton. 

.2314 and 4.32. .2314 is used instead of 
because 7000 (grains) divided by 36 



36X840 

(inches per yard) and 840 (yards) equals .2314. 

4.32 is used instead of — because 

36X840 divided by 7000 equals 4.32. 

764. This number is used in cloth calcula- 
tions instead of 840 to allow for contraction in 
length and width, also for size or dressing on 
the warp yarns. All cloths contract in length 
and width to a greater or less degree, making 
it necessary to allow a certain amount of extra 
length of yarn for a given length or width of 
cloth. The 764 allows (adds) 10%. 

10% of 764 == 76, and 764 + 76 = 840. 

The constant 764 cannot be used for all classes 
of goods because the factors mentioned above 



10 PRACTICAL COTTON CALCULATIONS 

will vary in amount in different cloths. For 
very coarse goods, or cloths where sizing is added 
to give weight, a lower constant mnst be used. 

The rules in which the constant 764 appears 
have been proved practical for cloths ranging in 
counts of yarn from 50 's to 70 's, and in counts 
of cloth from 60 to 80, the warp and filling in 
any one cloth, and the sley and pick being nearly 
equal. 

For some constructions of cloth the constant 
764 will have to be substituted by another, 
higher or lower, according to whether the con- 
traction is small or great. 

As perhaps all persons who have occasion to 
use the rules containing the constant 764 will 
have access to a weave room, it is advisable that 
they select a few styles that vary in structure, 
i. e., that vary in the sley as compared to the 
pick, or in warp as compared to filling, and 
note the difference in contraction, if any, and 
the cause of the same. From data obtained in 
this manner constants may be formulated that 
can be used in future when dealing with other 
cloths of approximately similar constructions. 
In this connection it will be well to bear in mind 
the various modifying factors explained under 
the headings Cloth Contraction and Reed Cal- 
culations. 

With the exception of rules 3, 58, 60, 61, 62, 
63, 80, 81 and those indicated with a *, the rules 
in this book may be used to aid in solving prob- 
lems connected with other textile materials as 
well as cotton. 



YARN CALCULATIONS, 



LENGTH AND WEIGHT STANDARDS. 

The following standards are used when dealing 
with cotton calculations: 

Standard of Lengths for Cotton. 

If yds. = The circumference of reel, or lwrap. 
120 yds. = 1 lea, or 80 wraps of the reel. 
840 yds. = 7 leas, or 1 hank. 

Standard of Weights for all Textile Materials. 

437.5 grains = 1 ounce, avoirdupois. 
7000 grains = 16 ozs., or 1 pound. 

The counts of cotton yarns are based on the 
number of times that the standard of length, 840 
yards, is contained in the length of yarn required 
to balance the standard of weight, 1 pound; thus, 
if 840 yards of yarn balance lib, the counts 
are l's. 

If 4200 yards of yarn balance lit), the counts 
are 5's, because 4200 -f- 840 = 5 ; and so on, the 
higher the counts the more yards per pound, 
therefore the higher the counts the finer the 
yarn. See page 33 for table of counts and 
yards per pound of cotton yarns. 



12 PRACTICAL COTTON CALCULATIONS 

TESTING YARNS FOR COUNTS, BY COMPARI- 
SON. 

When analyzing small cloth samples, the 
average counts of the yarn may readily be found 
from the cloth by Rule 49. 

In some cases the warp and filling may vary 
considerably in counts, making it necessary to 
find the counts of each separately. The counts 
of the warp yarn is generally found, the mills 
usually using but few different warp counts, and 
varying the weights of the cloths by changing 
the counts of the filling, if necessary, because it 
is more practical and convenient. Although 
short method No. 1, on the following page, may 
be applied for finding the counts of the yarn by 
weighing a few inches, the most practical method 
is by comparing the warp yarn from the cloth 
with warp yarns of known counts. 

A B 

zzazzzzzzzz2zzzzzzzzzzzzr& ; 



ZZZ 



uiititittttttittuiiujyj* 
fffffffffeffffnii mzzzjQcz 



Fig. 1. 



B 



Fig. 2. 

Fig. 1 illustrates the method of testing known 
with unknown counts; "A" represents the 
known and "B" the unknown counts. To get 
the yarns as here shown place one or more yarns 



PRACTICAL COTTON CALCULATIONS 13 

of the known at right angles to the unknown 
counts, and twist them, making, as it were, one 
continuous yarn. If one yarn is coarser than 
the other, it can readily be seen, after twisting. 
Fig. 2 shows the yarns in Fig. 1 after being- 
twisted. It is advisable to wet the yarns, at the 
point where they are crossed, before twisting. 

The greater the number of strands of each 
count used, the less the liability to error. 

This method of testing is used practically, 
because a mill usually uses the nearest counts of 
warp yarn that they have on hand to the counts 
of the warp in the sample if they intend to 
duplicate it. 

Some persons do not care to trust the naked 
eye when comparing yarns, but prefer to use a 
magnifying glass of some kind, such as a pick 
glass, reading glass, or microscope. 

TESTING YARNS FOR COUNTS, BY WEIGH- 
ING SHORT LENGTHS. 

1. The number of inches that weigh 
1 gr. X .2314 = Counts. 

2. The number of strands of yarn, each 4 fl- 
inches or 4.32 inches long that weigh 1 grain = 
Counts. 

3. Number of yards weighed X 8 J -f- weight 
in grains = Counts. 

4. Number of yards weighed -j- .12 X weight 
in grains = Counts. 

5. 1000 divided by weight in grains of 1 lea 
= Counts. 



14 PRACTICAL COTTON CALCULATIONS 

REELING YARNS. 

To Find Counts of Yarn from Any Number of 
Yards Reeled or Measured. 

*Rule 1. Multiply the number of yards reeled 
by 84, and divide by the weight in grains. 

Example. 10 yards of cotton yarn weigh 
2 grains. What are the counts? 

10 yds. X 8.333 < ., 

- = 41. bb s counts, Ans. 



2 grs. 

or by "Rule 2. Divide the number of yards 
r< < led by .12 and the weight in grains. 
Example. Same as preceding. 

10 yds. tH nn . . 

— — — =- — — = 41.66 s counts, Ans. 
.12 X 2 grs. 

Rules 1 and 2 will apply when desiring 

To Find the Number of Hank of Roving. 



To Find Counts of Yarn from Bobbins or Cops. 

Reel one lea each from 1, 2, 3, or 4 bobbins 
or cops, and use — 

Rule 3. Add 3 ciphers to the number of leas 
reeled and divide by the weight of the yam in 
grains. 

Example. s One lea is reeled from each of 
4 bobbins and found to weigh 50 grains. What 
are the counts? 



PRACTICAL COTTON CALCULATIONS 15 

4000^-50 grs. = 80's counts, Ans. 

In the above rule \ of a hank is considered in 
connection with a corresponding portion of a 
pound, i. e., } of 7000 grains = 1000 grains. If 
1 lea is reeled from each of 4 bobbins, then 4 leas 
are reeled, or f of a hank. As f of a hank is 
weighed, the weight must be divided into 4000 
grains, or f of a pound. 

The principal reasons why 1 lea is reeled from 
each of 4 bobbins in preference to 4 leas from 
1 bobbin, or 1 lea from 1 bobbin, are that the 
yarn may be reeled on an ordinary reel from 
4 bobbins at a time, thus saving time, and a 
better average may be obtained, as there is 
greater liability for the yarn to vary in size on 
4 bobbins than on 1 bobbin. 

On the four following pages Draper's cotton 
yarn numbering tables are reproduced by per- 
mission of the Draper Co., Hopedale, Mass. 
These tables are based on the weight in grains 
of 1 lea, or 120 yards. 

If more than one bobbin or cop is used, and 
more than one lea weighed, divide the weight 
in grains by the number of leas. 

Example. One lea is reeled from each of 
4 bobbins, and found to weigh 50 grains. 
What are the counts ? 

50 ^- 4 = 12.5 grains per lea, which shows on 
the table to be 80 's yarn. 



16 PRACTICAL COTTON CALCULATIONS 

Table for numbering Cotton Yarn by the weight in g'rains of 
120 yards or I skein. 



120yds 


Number 


120yds Number 


120yds. 


Number 


120yds Number 


120yds. 


Number 


weigh 


of 


weigh 


of 


weigh 


of 


weigh 


of 


weigh 


of 


grains. 


Yam. 


grains. 


Yarn. 


grains 


Yarn. 


grains 


Yarn 


grains. 


Yarn. 


1. 


1000. 


14. 


71.43 


21 


47.62 


28. 


35.71 


35. 


28.57 


2. 


500. 


.1 


70.92 


.1 


47.39 


.1 


35.59 


.1 


28.49 


3. 


333.3 


2 


70.42 


2 


47.17 


.2 


35.46 


.2 


28.41 


4. 


250.0 


3 


69.93 


3 


46.95 


.3 


35.34 


.3 


28.33 


5. 


200.0 


4 


69.44 


.4 


46.73 


.4 


35.21 


.4 


28.25 


5.5 


181.8 


.5 


68.97 


5 


46.51 


.5 


35.09 


.5 


28.17 


6. 


166.7 


.6 


68.49 


6 


46.30 


.6 


34.97 


.6 


28.09 


6.5 


153.8 


.7 


68.03 


.7 


46.08 


.7 


34.84 


.7 


28.01 


7. 


142.9 


.8 


67.57 


8 


45.87 


.8 


34.72 


.8 


27.93 


7.5 


133.3 


.9 


67.11 


.9 


45.66 


.9 


34.60 


.9 


27.86 


8. 


125.0 


15. 


66.07 


23. 


45.45 


29 


34.48 


36 


27.78 


1 


123.5 


.1 


66.23 


.1 


45.25 


.1 


34.36 


.1 


27.70 


2 


122.0 


.2 


65.79 


.2 


45.05 


.2 


34.25 


.2 


27.62 


3 


120.5 


3 


65.36 


.3 


44.84 


.3 


34.13 


.3 


27.55 


4 


119.0 


.4 


64.94 


.4 


44.64 


4 


34.01 


.4 


27.47 


5 


117.6 


.5 


64.52 


.5 


44.44 


.5 


33.90 


.5 


27.40 


6 


116.3 


6 


64.10 


.6 


44.25 


.6 


33.78 


.6 


27.32 


7 


114.9 


7 


63.69 


.7 


44.05 


7 


33.67 


7 


27.25 


.8 


113.6 


.8 


63.29 


.8 


43.86 


.8 


33.56 


.8 


27.17 


.9 


112.4 


.9 


62.89 


.9 


43.67 


.9 


33.44 


.9 


27.10 


9. 


111.1 


16 


62.50 


23- 


43.48 


30 


33.33 


37 


27.03 


1 


109.9 


1 


62.11 


.1 


43.29 




33.22 


1 


26.95 


2 


108.7 


2 


61.73 


.2 


43.10 


.2 


33.11 


.2 


26.88 


3 


107.5 


3 


61.35 


.3 


42.92 


.3 


:'.:>,.< in 


.3 


26.81 


4 


106.4 


4 


60.98 


.4 


42.74 


.4 


32.89 


.4 


20.74 


5 


105.3 


.5 


60.61 


5 


42.55 


.5 


32.79 


.5 


20.67 


6 


104.2 


6 


60.24 


.6 


42.37 


.6 


32.68 


.6 


20..60 


.7 


103.1 


7 


59.88 


7 


42.19 


.7 


32.57 


.7 


20.53 


.8 


102.0 


.8 


59.52 


.8 


42.02 


.8 


32.47 


.8 


20.46 


.9 


101.0 


.9 


59.17 


.9 


41.84 


.9 


32.36 


.9 


26.39 


to 


100.0 


17. 


58.82 


24. 


41.67 


31 


32.26 


38. 


20.32 


.1 


99.01 


.1 


58.48 


1 


41.49 


.1 


32.16 


.1 


26.25 


.2 


98.04 


2 


58.14 


2 


41.32 


.2 


32.05 


.2 


26.18 


.3 


97.09 


3 


57.80 


3 


41.15 


.3 


31.95 


.3 


2(5.11 


.4 


96.15 


4 


57.47 


4 


40.98 


.4 


31.85 


.4 


20.04 


5 


95.24 


5 


57.14 


5 


40.82 


.5 


31.75 


.5 


25.D7 


6 


94.34 


6 


56.82 


.6 


40.65 


.6 


31.65 


.6 


25.91 


7 


93.46 


7 


56.50 


.7 


40.49 


7 


31.55 


.7 


25.84 


8 


92.59 


.8 


56.18 


.8 


40.32 


.8 


31.45 


.8 


25.77 


9 


91.74 


.9 


55.87 


9 


40.16 


.9 


31.35 


.9 


25.71 


11. 


90.91 


18. 


55.56 


25. 


40.00 


32. 


31.25 


39. 


25.04 


1 


90.09 


1 


55. 25 


1 


39.84 


.1 


31.15 


.1 


25.58 


2 


89.29 


2 


54.95 


.2 


39.68 


.2 


31.06 


.2 


25.51 


3 


88.50 


3 


54.64 


3 


39.53 


.3 


30.96 


.3 


25.45 


4 


87.72 


4 


54.35 


4 


39.37 


.4 


30.86 


4 


25.38 


5 


86.96 


.5 


54.05 


5 


39.22 


.5 


30.77 


5 


25.32 


6 


86.21 


.6 


53.76 


.6 


39.06 


6 


30.67 


.6 


25.25 


.7 


85.47 


.7 


53.48 


.7 


38.91 


7 


30.58 


.7 


25.19 


.8 


84.75 


.8 


53.19 


.8 


38.76 


.8 


30.49 


.8 


25.13 


.9 


84.03 


9 


52.91 


9 


38.61 


.9 


30.40 


.9 


25.06 


12. 


83.33 


19. 


52.63 


26. 


38.46 


33. 


30.30 


*0. 


25.00 


1 


82.64 


.1 


52.36 




38.31 


.1 


30.21 


.1 


24.94 


.2 


81.97 


.2 


52.08 


.2 


38.17 


.2 


30.12 


£ 


24.88 


.3 


81.30 


.3 


51.81 


3 


38.02 


.3 


30.03 


.ft 


24.81 


.4 


80.65 


4 


51.55 


4 


37.88 


.4 


29.94 


.4 


24.75 


.5 


80.00 


.5 


51.28 


5 


37.74 


.5 


29.85 


.5 


24.69 


.6 


79.37 


.6 


51.02 


.6 


37.59 


.6 


29.76 


.6 


24.63 


.7 


78.74 


.7 


50.76 


.7 


37.45 


.7 


29.67 


.7 


24.57 


8 


78.12 


.8 


50.51 


.8 


37.31 


.8 


29.59 


.8 


24.51 


.9 


77.52 


.9 


50.25 


.9 


37.17 


.9 


29.50 


.9 


24.45 


13. 


76.92 


30. 


50.00 


27- 


37.04 


34. 


29.41 


41. 


24.39 


.1 


76.34 


.1 


49.75 


.1 


36.90 


.1 


29.33 


.1 


24.33 


.2 


75.76 


.2 


49.50 


.2 


36.77 


.2 


29.24 


.2 


24.27 


.3 


75.19 


.3 


49.26 


.3 


36.63 


.3 


29.15 


.3 


24.21 


.4 


74.63 


.4 


49.02 


.4 


36.50 


.4 


29.07 


.4 


24.15 


.5 


74.07 


.5 


48.78 


.5 


36.36 


.5 


28.99 


.5 


24.10 


.6 


73.53 


.6 


48.54 


.6 


36.23 


.6 


28.90 


.6 


24.04 


.7 


72.99 


.7 


48.31 


.7 


36.10 


.7 


28.82 


.7 


23.98 


.8 


72.46 


.8 


48.08 


.8 


35.97 


.8 


28.74 


.8 


23.92 


.9 


71.94 


.9 


47.85 


.9 


35.84 


.9 


28.65 


.9 


23.87 



PRACTICAL COTTON CALCULATIONS 



17 



Table tor numbering Cotton Yarn by the weight 
120 yards or I skein. 



120yda 


Number 


120yds 'Number 


120yds 


Number 


120yds 


Number 


120yds Number 


weigh 


of 


weigh 


of 


weigh 


of 


weigh 


of 


weigh 


of 


grains. 


YUI-D. 


graius 


Yarn. 


graius 


Yaru 


graius 


Yaru 


grains. 


Yarn 


42. 


23.81 


49. 


20.41 


56 


17.86 


63 


15.87 


70. 


14.29 


.1 


23.75 




20.37 


.1 


17.83 


.1 


15.85 


.1 


14.27 


.2 


23.70 


'.2 


20.33 


2 


17.79 


.2 


15.83 


.2 


14.25 


.3 


23.G4 


.3 


20.28 


.3 


17.70 


.3 


15.80 


.3 


14.22 


.4 


23.58 


.4 


2H.24 


.4 


17.73 


.4 


15.77 


.4 


14.2< 


.5 


23.53 


.5 


20.20 


.5 


17.70 


.5 


15.75 


.5 


14.18 


.6 


23.47 


.6 


20.10 


.0 


17.67 


.6 


15.72 


.0 


14.1f, 


.7 


23.42 


.7 


20.12 


.7 


17.04 


.7 


15.70 


.7 


14.14 


.8 


23.3H 


.8 


20.08 


.8 


17.G1 


.8 


15.87 


.8 


14.12 


.9 


23.31 


.9 


20.04 


.9 


17.57 


.9 


15.65 


.9 


14.10 


43. 


23.20 


50. 


20.00 


57- 


17.54 


64. 


15.62 


71. 


14.08. 


.1 


23.20 


.1 


19.90 


.1 


17.51 


.1 


15.00 


.1 


14.06 


.2 


23.15 


.2 


19.92 


,2 


17.48 


.2 


15.58 


.2 


14.04 


.3 


23.09 


.3 


19.88 


.3 


17.45 


.3 


15.55 


.3 


14.03 


.4 


23.04 


.4 


1 9.84 


.4 


17.42 


.4 


15.53 


.4 


14.01 


.5 


22.99 


.5 


19.80 


.5 


17.39 


.5 


l5.5ti 


.5 


13.99 


.0 


22.94 


.6 


19.76 


.6 17.36 


.6 


15.48 


.6 


13.97 


.7 


22.88 


.7 


19.72 


.7 


17.33 


.7 


15.46 


.7 


13.95 


.8 


22.83 


.8 


19.09 


.8 


17.30 


.8 


15.43 


.8 


13.93 


.9 


22.78 


.9 


19.05 


.0 


17.27 


.9 


15.41 


.9 


13.91 


44. 


22.73 


51 


19.61 


58. 


17.24 


65. 


15.38 


TA. 


13.89 


.1 


22.08 


.1 


19.57 


.1 


17.21 


.1 


15.30 


.1 


13.87 


.2 


22.02 


. .2 


19.53 


.2 


17.18 


.2 I 15.34 


.2 


13.85 


.3 


22.57 


.3 


19.49 


.3 


17.15 


.3 15.31 


.3 


13.83 


.4 


22.52 


.4 


19.46 


.4 


17.12 


.4 


15.29 


.4 


13.81 


.5 


22.47 


.5 


19.42 


.5 


17.09 


.5 


15.27 


.6 


13.79 


.6 


22.42 


.6 


19.38 


.6 


17.06 


.6 


15.24 


.6 


13.77 


.7 


22.37 


.7 


19.34 


.7 


17.04 


.7 


15.22 


.7 


13.76 


.8 


22.32 


.8 


19.31 


.8 


17.01 


.8 


15.20 


.8 


13.74 


.9 


22.27 


.9 


19.27 


.9 


16.98 


.9 


15.17 


.9 


13.72 


45. 


22.22 


554. 


19.23 


59 


16.95 


6b 


15.15 


7& 


13.70 


.1 


22.17 


.1 


19.19 




16.92 


.1 


15.13 


.1 


13.68 


.2 


22.12 


.2 


19.16 


.2 


16.89 


.2 


15.11 


.2 


13.66 


.3 


22.08 


.3 


19,12 


.3 


16.86 


.3 


15.08 


.3 


13.64 


.4 


22.03 


.4 


19.08 


.4 


16.84 


.4 


15.06 


.4 


13.02 


.5 


21.98 


.5 


19.05 


.5 


16.81 


.5 


15.04 


.6 


13.61 


.0 


21.93 


.6 


19.01 


.6 


16.78 


.0 


15.02 


.6 


13.59 


.7 


21.88 


.7 


18.98 


.7 


16.75 


.7 


14.99 


.7 


13.57 


.8 


21.83 


.8 


18.94 


.8 


16.72 


.8 


14.97 


.8 


13.55 


.11 


21.79 


.9 


18.9(i 


.9 


10.6!j 


.9 


14.95 


9 


13.53 


4b 


21.74 


53. 


18.87 


00. 


16.67 


67. 


14.93 


74. 


13.51 


.1 


21.69 


.1 


18.83 


.1 


16.64 


.1 


14.90 


.1 


13.50 


.2 


31.85 


'.2 


18.80 


.2 


16.61 


.2 


14.88 


.2 


13.48 


.3 


21.60 


.3 


18.70 


.3 


16.58 


.3 


14.80 


.3 


13.40 


.4 


21.55 


.4 


18.73 


.4 


10.5< 


A 


14.84 


.4 


13.44 


.5 


.'1.51 


.5 


°1 8.011 


.5 


16.53 


.6 


14.81 


.6 


13.42 


.0 


31,46 


.6 


18.00 


.6 


16.51 


.0 


14.79 


.0 


13.40 


.7 


21.41 


.7 


18.62 


.7 


16.47 


.7 


14.77 


.7 


13.39 


.8 


31.37 


.8 


18.59 


.8 


16.45 


.8 


14.75 


.8 


13.37 


.9 


21.32 


.9 


18.55 


.9 


16.42 


.9 


14.73 


.9 


13.35 


4? 


21.28 


54. 


in. 52 


61. 


10.39 


68. 


14.71 


76. 


13.33 


.1 


21.23 


.1 


18.48 


.1 


10.37 


.1 


1 4.08 


.1 


13.32 


.2 


21.1 9 


.2 


18.45 


.2 


10.34 


.2 


1 4.6b 


.2 


13.3o 


.3 


21.14 


.3 


18.42 


.3 


10.31 


.3 


14.04 


.3 


13.28 


.4 


21.10 


.4 


18.38 


.4 


16.29 


.4 


14.62 


.4 


13.20 


.6 


21.05 


.5 


18.35 


.5 


16.26 


.5 


14.00 


.5 


13.25 


.6 


21.01 


.6 


18.32 


.6 


16.23 


.0 


14.58 


.0 


13.23 


.7 


20.90 


.7 


18.28 


7 


10.21 


.7 


14.50 


.7 


13.21 


.8 


20.92 


.8 


18.25 


.8 


16.19 


.8 


14.53 


.8 


13.19 


.9 


20.8.S 


.9 


18.21 


9 


16.16 


.9 


14.51 


.9 


13.18 


«b. 


20.83 


55. 


18.18 


ua 


10.13 


6b 


14.411 


7b 


13.10 




20.79 


.1 


18.15 




10.10 




14.47 


.1 


13 14 


'.2 


20.75 


.2 


18.12 


'§ 


10.08 


'.2 


14.45 


.2 


13.12 


.3 


20.70 


t 


18. 08 


.3 


10.05 


.3 


14.43 


.3 


13.11 


.4 


2O.C0 


18.05 


.4 


10.03 


.4 


14.41 


.4 


13.09 


.5 20.02 


.6 


IS. 02 


.5 


16.00 


.5 


14.39 


,6 


13.07 


.6 1 20.57 


.6 


17.99 


.6 


15.97 


.0 


14.37 


.0 


13.05 


.7 I 20.53 


.7 


17.95 


7 


15.95 


7 


14.35 


.7 


13.IM 


.8 20.49 


.8 


17 92 


.8 


15.92 


.8 


14.33 


.8 


13.02 


.9 20.45 


.9 


17.89 




16.90 


.9 


14.31 


.9 


13.00 



18 



PRACTICAL COTTON CALCULATIONS 



Table for numbering Cotton Vam by the weight in grains of 
120 yards or I skein 



120yds. 


Number 


liOvds 


Number 


120vds 


Number 


120>ds 


Number 


l^OvJs 


Number 


weigh 


of 


weigh 


of 


weigh 


of 


weigh 


ol 


weigh 


of 


grains. 


Yarn 


grains 


Yarn 


grains 


Yarn 


grains 


Yarn 


grains. 


Yarn 


77. 


12.99 


84 


11.90 


91. 


10.99 


98. 


10.20 


105. 


9.52 


.1 


12.97 


.1 


11.89 


.1 


10.98 


.1 


10.19 


.1 


9.51 


.2 


12.95 


.2 


11.88 


.2 


10.90 


.2 


10.18 


.2 


9.51 


.3 


12.94 


.3 


11.80 


.3 


10.95 


.3 


10.17 


.3 


9.50 


.4 


12.92 


.4 


11.85 


.4 


10.94 


.4 


10.10 


.4 


9.49 


.5 


12.90 


.5 


11.83 


.5 


10.93 


.5 


10.15 


.5 


9.48 


.li 


12.89 


.0 


11.82 


.6 


10.92 


.0 


10.14 


.0 


9.47 


.7 


1 2.87 


.7 


11.81 


.7 


10.91 


.7 


10.13 


.7 


9.40 


.8 


12.85 


.8 


11.79 


.8 


10.89 


.8 


10.12 


.8 


9.45 


.9 


12.84 


.:> 


11.78 


.9 


10.88 


.9 


10.11 


.9 


9.44 


78. 


1 2.S2 


85. 


11.76 


92. 


10.87 


99. 


10.10 


106. 


9.43 




12.80 


.1 


11.75 


.1 


lO.HO 


:i 


10.0& 


.1 


9.43 


'.2 


12.79 


.2 


11.74 


.2 


10.85 


.2 


10.08 


.2 


9.42 


.3 


12.77 


3 


11.72 


.3 


10. «3 


.3 


10.07 


.3 


9-41 


.4 


1 2.7G 


.4 


11.71 


.4 


10.82 


.4 


10.00 


.4 


9.40 


.5 


12.74 


.5 


11.70 


.5 


10.81 


.5 


10.05 


.5 


9.39 


.6 


12.72 
12.71 


.0 


1 1.08 


.0 


10.80 


.0 


10.04 


.6 


9.38 


.7 


.7 


1 1 .07 


7 


10.79 


.7 


10-03 


.7 


9-37 


.8 


12.09 


.8 


11.66 


.8 


10.78 


.8 


10.02 


.8 


9.36 


.9 


12.07 


.9 


11.64 


9 


10.70 


9 


10-01 


9 


9-35 


79. 


12.00 


86. 


11.03 


93. 


10.75 


100. 


10.00 


107. 


9.35 


.1 


12.04 


.1 


11.01 


.1 


10.74 


.1 


9.99 


.1 


9.34 


.2 


12.03 


.2 


11.00 


3. 


10.73 


2 


9.98 


.2 


933 


.3 


12.G1 


.3 


11.59 


3 


10.72 


.3 


9.97 


.3 


9-32 


.4 


12.59 


.4 


11.57 


.4 


10.71 


.4 


9-96 


.4 


9-31 


.6 


12.58 


.5 


11.50 


5 


10.70 


:I 


9.95 


.5 


9.30 


.6 


12.50 


.6 


11.55 


6 


10.68 


9-94 


.6 


9-29 


.7 


12.55 


.7 


11.53 


.7 


10.67 


.7 


9.93 


.7 


9.29 


.8 


12.53 


.8 


11.52 


.8 


10.60 


.8 


9.92 


.8 


9.28 


9 


12.52 


.9 


11.51 


9 


10.65 


.9 


9.91 


9 


9-27 


80. 


12.50 


87. 


11.49 


94. 


10.64 


101. 


9.90 


108. 


9-26 


.1 


12.48 


.1 


11.48 


.1 


10.03 


.1 


9.89 


.1 


9-26 


.2 


12.47 


.2 


11.47 


.2 


10.02 


.2 


9.88 


.2 


924 


.3 


12.45 


.3 


11.45 


3 


10.00 


.3 


9.87 


.3 


9-23 


.4 


12.44 


.4 


11.44 


4 


10.59 


.4 


9.86 


.4 


9-23 


.6 


12.42 


.5 


11.43 


.5 


10.58 


.5 


9.85 


.5 


9.22 


.6 


12.41 


.6 


11.42 


.6 


10.57 


.6 


9.84 


.6 


9.21 


.7 


12-39 


.7 


11.40 


.7 


10.50 


.7 


9-83 


.7 


9-20 


.8 


12.38 


.8 


11.39 


.8 


10.55 


.8 


9.82 


.8 


9.19 


.9 


12.30 


9 


11.38 


9 


10.54 


9 


9.81 


.9 


9.18 


81 


12.35 


88 


11.30 


95- 


10.53 


102. 


9.80 


109. 


9.17 


.1 


12.33 


1 


11.35 


1 


10.52 


.1 


9.79 


.2 


9.10 


.2 


12.32 


.2 


11.34 


2 


10.50 


.2 


9.78 


.4 


9.14 


.3 


12.30 


.3 


11.33 


.3 


10.49 


.3 


9.78 


.6 


9.12 


.4 


12.29 


.4 


11.31 


4 


10.48 


.4 


9.77 


.8 


9.11 


.5 


12.27 


.5 


11.30 


.5 


10.47 


.5 


9.70 


110. 


9.09 


.6 


12-25 





11.29 


.0 


10.46 


6 


9.75 


.2 


9.07 


7 


12.24 


.7 


11.27 


7 


10.45 


.7 


9.74 


.4 


9.06 


.8 


12-22 


.8 


1 1 .20 


.8 


10.44 


.8 


9.73 


.6 


9.04 


.9 


12.21 


9 


11.25 





10.43 


.£> 


9.72 


.8 


9.03 


82- 


12-20 


89 


1 1.24 


96 


10.42 


103 


9.71 


111. 


9.01 


.1 


12.18 


1 


11.22 


.1 


10.41 


.1 


9.70 


.2 


8.99 


2 


12.17 


.2 


11.21 


.2 


10.40 


.2 


9.09 


.4 


8.98 


.3 


12.15 


.3 


11.20 


.3 


10.38 


.3 


9.08 


.6 


8.90 


.4 


12.14 


.4 


11.19 


.4 


10.37 


.4 


9.07 


.8 


8.94 


.5 


12.12 


.5 


11.17 


.5 


10.30 


.5 


9.06 


112. 


8.93 


.6 


12-11 


.6 


11.10 


.6 


10.35 


.6 


9.65 


.2 


8.91 


.7 


12.09 


.7 


11.15 


.7 


10.34 


.7 


9.64 


.4 


8.90 


.8 


12.08 


.8 


11.14 


.8 


10.33 


.8 


9.63 


.6 


8.88 


.9 


12.06 


9 


11.12 


.9 


10.32 


.9 


9.G2 


.8 


8.87 


83. 


12.05 


90. 


11.11 


97 


10.31 


104. 


9.02 


113. 


8,85 


.1 


12.03 


.1 


11.10 


.1 


10.30 


.1 


9.61 


.2 


8.83 


.2 


12.02 


.2 


11.09 


.2 


10.29 


.2 


9.60 


.4 


8.82 


.3 


12.00 


.3 


11.07 


.3 


10.28 


.3 


9.59 


.6 


8.80 


.4 


11.99 


.4 


11.06 


.4 


10.27 


.4 


9.58 


.8 


8.79 


.5 


11.98 


.6 


11.05 


.5 


10.20 


.5 


9.57 


114. 


8.77 


.6 


11.96 


.0 


11.04 


.6 


10.25 


.6 


9.56 


.2 


8.70 


.7 


11.95 


.7 


11.03 


.7 


10.24 


.7 


9.55 


4 


8.74 


.8 


1 1 .93 


.8 


11.01 


.8 


10.22 


.8 


9.54 


.6 


8.73 


.9 


11.92 


.9 


11.00 


.9 


10.21 


.9 


9.53 


.8 


8.71 



PRACTICAL COTTON CA I.Cl I.ATIONS 



l'.l 



Table for numbering Cotton Yarn by the weight in grains of 
120 ^yards or I skein 



120>>ls 


Number 


120yds 


Number 


I20.yds 


Number 


120vds 


Number 


120N.IS 


Number 


weigh 


of 


weigh 


of 


weigh 


of 


we.gh 


of 


wei^h 


of 


graius. 


Yarn 


grains. 


Yarn. 


grains. 


Yarn. 


grains. 


Yarn 


grains 


Yarn. 
2.50 


115. 


8.70 


140. 


7.14 


180. 


5.56 


250 


4.00 


400. 


.2 


8.68 


.5 


7.12 


181. 


5.52 


252. 


3.97 


405. 


2.47 


.4 


8.67 


141. 


7.09 


182. 


5.40 


254. 


3.94 


410. 


2.44 


.6 


8.65 


.5 


7.07 


183. 


5.40 


256. 


3.91 


415. 


2.41 


.8 


8.64 


142. 


7.04 


184. 


5.43 


258. 


3.88 


420. 


2.38 


116. 


8.62 


.5 


7.02 


185. 


5.41 


200. 


3.85 


425. 


2.35 


.2 


8.61 


143. 


6.99 


186. 


5.38 


202. 


3.82 


430. 


2.3H 


.4 


8.59 


.5 


6.97 


187. 


5.35 


264. 


3.79 


435. 


2.30 


.6 


8.58 


144. 


6.94 


1 ss. 


5.32 


260. 


3.76 


44H. 


2.27 


.8 


8.56 


.5 


6.92 


189. 


5.29 


268. 


3.73 


445. 


2.25 


117. 


8.55 


145. 


6.90 


190. 


5.26 


270. 


3.70 


450. 


2.22 


.2 


8.53 


.5 


6.87 


191. 


5.24 


272. 


3.68 


455. 


2.20 


.4 


8.52 


140. 


6.85 


192. 


5.21 


274. 


3.65 


460. 


2.17 


.6 


8.50 


.5 


6.83 


193. 


5.18 


276. 


3.62 


405. 


2.15 


.8 


8.49 


147. 


6.80 


194. 


5.15 


278. 


3.60 


470. 


2.13 


118. 


8.47 


.5 


6.78 


195. 


5.13 


280. 


3.57 


475. 


2.11 


.2 


8.46 


148. 


6.76 


196. 


5.10 


282. 


3.55 


480. 


2.08 


.4 


8.45 


.5 


6.73 


197. 


5.08 


284. 


3.52 


485, 


2.00 


.0 


8.43 


149. 


6.71 


198 


5.05 


280. 


3.50 


490. 


2.04 


.8 


8.42 


.5 


6.69 


199. 


5.03 


288. 


3.47 


495. 


2.02 


119. 


8.40 


150. 


6.67 


300 


5.00 


290. 


3.45 


500. 


2.00 


.2 


8.39 


.5 


6.64 


201. 


4.98 


292. 


3.42 


505. 


1.98 


.4 


8.38 


151. 


6.62 


202. 


4.95 


294. 


3.40 


510. 


1.96 


.6 


8.36 


.5 


6.60 


203. 


4.93 


290. 


3.38 


515. 


1.94 


.8 


8.35 


152. 


6.58 


204 


4.90 


298 


3.36 


520. 


1.92 


120. 


8.33 


.5 


6.56 


205. 


4.88 


300. 


3.33 


525. 


1.90 


.2 


8.32 


153. 


6.54 


206. 


4.85 


3(12. 


3.31 


530. 


1.89 


.4 


8.31 


5 


6.51 


207. 


4.83 


304. 


3.29 


535. 


1.87 


.6 


8.29 


154. 


6.49 


208. 


4.81 


306. 


3.27 


540. 


1.85 


.8 


8.28 


5 


6.47 


209. 


4.78 


308. 


3.25 


545. 


1.83 


121. 


8.26 


155. 


6.45 


210. 


4.70 


310 


3.23 


550. 


1.82 


.4 


8.24 


.5 


6.43 


211. 


4.74 


312 


3.21 


555. 


1.80 


.6 


8.22 


156. 


6.41 


212. 


4.72 


314. 


3.18 


500. 


1.79 


.8 


8.21 


.5 


6.39 


213. 


4.09 


316. 


3.17 


505. 


1.77 


122. 


8.20 


157. 


6.37 


214. 


4.07 


318. 


3.14 


570. 


1.75 


.5 


8.16 


.5 


6.35 


2 1 5. 


4.65 


320. 


3.12 


575. 


1.74 


123. 


8.13 


158. 


6.33 


216. 


4.63 


322. 


3.11 


580. 


1.72 


5 


8.10 


5 


6.31 


217. 


4.61 


324. 


3.09 


585. 


1.71 


124. 


8.06 


159. 


6.29 


218. 


4.59 


320. 


3.07 


500. 


1.00 


.5 


8.03 


5 


6.27 


219. 


4.57 


328. 


3.05 


595. 


1.68 


125. 


8.00 


160. 


6.25 


220 


4.55- 


330 


3.03 


600. 


1.67 


.5 


7.97 


5 


6.23 


221 


4.52 


3:*, 2. 


3.01 


010. 


1.04 


126. 


7.94 


161. 


6.21 


222. 


4. 5H 


334. 


2.99 


020. 


1.61 


.5 


7.91 


5 


6.19 


223 


4.48 


336. 


2.98 


030. 


1.59 


127. 


7.87 


162. 


6.17 


224 


4.46 


338. 


2.96 


040. 


1.50 


■5 


7.84 


.5 


6.15 


225 


4.44 


340. 


2.94 


050. 


1.54 


128. 


7.81 


163. 


6.13 


226. 


4.42 


342. 


2.92 


660. 


1.52 


.5 


7.78 


5 


6.12 


227 


4.41 


344. 


2.91 


070. 


1.49 


129. 


7.75 


164. 


6.10 


228. 


4.39 


346 


2.89 


080. 


1.47 


5 


7.72 


.5 


6.08 


229 


4.37 


348 


2.87 


690. 


1.45 


130. 


7.09 


165. 


6.06 


3.30. 


4.35 


350 


2.86 


700. 


1.43 


5 


7.66 


.5 


6.04 


231. 


4.33 


352 


2.84 


710. 


1.41 


131. 


7.63 


166. 


6.02 


232 


4.31 


354. 


2.82 


720. 


1.39 


.5 


7.60 


.5 


6.01 


233. 


4.29 


350 


2.81 


730. 


1.37 


132. 


7.53 


167. 


5.99 


234 


4.27 


358 


2.79 


740. 


1.35 


.5 


7.55 


.5 


5.97 


235. 


4.26 


360. 


2.78 


750. 


1.33 


133. 


7.52 


168. 


5.95 


236. 


4.24 


302. 


2.76 


760. 


1.32 


.5 


7.49 


.5 


5.93 


237. 


4.22 


304. 


2.75 


770. 


1.30 


134. 


7.46 


169. 


5.92 


238. 


4.20 


306. 


2.73 


780. 


1.28 


.5 


7.43 


5 


5.90 


239. 


4.18 


368. 


2.72 


790. 


1.27 


136, 


7.41 


170. 


5.88 


240. 


4.17 


370 


2.70 


800. 


1.25 


.?» 


7.38 


171. 


5.85 


241. 


4.15 


372. 


2.69 


820. 


1.22 


13G. 


7.35 


172 


5.81 


242. 


4.13 


374. 


2.07 


840. 


1.19 


.5 


7.33 


173. 


5.78 


243. 


4.12 


376. 


2.66 


800. 


1.16 


137. 


7.30 


174. 


5.75 


244. 


4.10 


378. 


2.65 


880. 


1.14 


.5 


7.27 


175. 


5.71 


245. 


4.08 


380. 


2.03 


900. 


1.11 


138. 


7.25 


176. 


5.68 


246. 


4.07 


382. 


2.02 


925. 


1.08 


.5 


7.22 


177. 


5.65 


247. 


4.05 


385. 


2.60 


950. 


1 .05 


139. 


7.19 


178. 


5.62 


248. 


4.03 


390. 


2.56 


075. 


1.03 


.6 


7.17 


179. 


5. 5J) 


249 


4.0? 


395. 


2.53 


1000. 


1.00 



20 PRACTICAL COTTON CALCULATIONS 

SYSTEMS OF NUMBERING YARNS OF VA- 
RIOUS MATERIALS. 
The following systems, where higher counts 
indicate finer yarns, are used in the United 
States : 

Raw silk = number of yards per ounce. 
Spun silk — 840 yards per hank. 
Cotton = 840 yards per hank. 
Worsted = 560 yards per hank. 
Woolen = 1600 yards per rain. 
Woolen = 300 yards per cut. 
Linen = 3( M ) ya r( Is per cut. 
The cut system of woolen counts is principally 
used in the vicinity of Philadelphia. 

The yarn calculations applying' to cotton will 
also apply to any of the above systems, using 
their respective standard lengths instead of 840. 

EQUIVALENT COUNTS. 
To Find Equivalent Counts of Yarn from One 
System to Another. 
Rule 4. Multiply the given counts of yarn by 
its standard length and divide by tin standard 
length in the system desired. 

Example. What counts of worsted is equal 
to a 30 's cotton yarn? 
30 's counts X 840 cotton standard .-, 

560 worsted standard a ' 

Short Methods to Find Equivalent Counts of 

Yarn in Woolen, Worsted, Linen, Raw Silk, 

or Metric System of Counting Cotton to a 

Given United States Cotton Yarn. 

.525 X counts of cotton yarn = woolen counts, 

run system. 



PRACTICAL COTTON CALCULATIONS 21 

1.5 X counts of cotton yarn =worsted counts, 

hank system. 
2.8 X counts of cotton yarn = linen counts, 

cut system. 
2.8 X counts of cotton yarn = woolen counts, 

cut system. 
52.5 X counts of cotton yarn — raw silk counts, 

yds. per oz. system. 
1.69 X counts of cotton yarn = metric system 

of numbering cotton. 
Short Methods to Find Cotton Counts Equivalent 
to Any Given Counts of Woolen, Worsted, 
Linen, Raw Silk, or the Metric System of 
Counting Cotton Yarn. 
1.905 X counts of woolen yarn, run system. 
.857 X counts of woolen yarn, cut system. 
.357 X counts of linen yarn, cut system. 
.666 X counts of worsted yarn, hank system. 
.019 X counts raw silk yarn, yds. per. oz. system. 
.59 X counts of cotton in metric system= cot- 
ton counts in United States system. 
The preceding constants are obtained as follows : 
840 -r- 1600 = .525 for woolen, run system. 



840 -f- 


560 = 1.5 for worsted, hank system. 


840^ 


300 = 2.8 for linen and woolen, cut 




system. 


840-^ 


16 (ozs. per lb) =52.5 for raw silk. 




yds. per oz. system. 



1600 -f- 840 = 1.905 for woolen, run system. 
300 ~ 840= ..357 for linen and woolen, cut- 
system. 
560 r- 840= .666 for worsted, hank system. 
16 -r- 840 = .019 for raw silk, yds. per oz. 

system. 



22 PRACTICAL COTTON CALCULATIONS 

RAW SILK CALCULATIONS. 

Owing to the growing use of silk yarns in the 
finer grades of fabrics composed for the greater 
part of cotton, the relative silk and cotton stan- 
dards are here indicated. 

When a problem presents itself in which silk 
yarns have to be considered, first obtain the 
equivalent cotton counts and proceed according 
to the rules regarding cotton yarns and fabrics. 

In addition to the system of numbering raw 
silk by the number of yards per ounce, where 
higher numbers indicate finer yarns, there are 
two other systems used in America and Great 
Britain. These are known as the dram system 
and the denier system. They differ from the 
cotton and spun silk systems in having higher 
numbers indicate coarser yarns. 

The dram system is based on the weight in 
drams of 1000 yards of yarn. For example, a 
4-dram silk means that a length of 1000 yards 
of yarn weighs 4 drams. 

There are several so-called denier systems, 
but the one recognized by the New York and 
London conditioning houses, and one extensive- 
ly used in France, is based on the weight in 
deniers of a skein of 476 metres, or 520.56 yards. 
For example, a 19/21 denier raw silk means that 
a skein 520.56 yards long weighs from 19 to 21 
deniers. For calculation purposes a 19/21 yarn 
would be considered a 20 's yarn. The num- 
ber 520 is usually used instead .of 520.56. 

A denier is a small weight equal to .8196 of 
a. grain, or .02997 of a dram. 

The relative values of the dram, denier and 
grain standards of weights are as follows: 



PRACTICAL COTTON CALCULATIONS 23 

1 dram = 33^ deniers = 27.34 grains. 
16 drams = 533J deniers = 437.5 grains 

= 1 oz. 
256 drams = 8533 deniers = 7000 grains 

= 16 ozs. = 1 lb. 

Short Methods to Find Equivalent Counts in the 
Dram Silk, Denier Silk and Cotton Systems. 

304.76 -=- dram silk counts = cotton counts. 
5282 -=- denier silk counts = cotton counts. 
304.76 -~ cotton counts = dram silk counts. 
5282 —- cotton counts = denier silk counts, 
denier silk counts -=- 17.366 (17^) 

= dram silk counts, 
dram silk counts X 17.366 (17J) 

= denier silk counts. 
The preceding constants are obtained as fol- 
lows : 

256 grains X 1000 yards 

— nTF{ — — t — — =oU4.7o 
840 yards 

8533 deniers X 520 yards __ _ 

840 yards 

1000 yards : 1 dram : : 520.56 yards : 17.366 
deniers. 

If 1000 yards in the dram system weighs 1 
dram for No. l's yarn, 520.56 yards in the 
denier system will weigh 17.366 deniers for the 
same counts. 

17-J- is usually used instead of 17.366. 

The words "organzine" and "tram," used in 
connection with silk, refer to warp and filling 
yarn respectively. Organzine silk usually con- 
tains more fibres than tram silk, and is harder 
twisted. 



24 PRACTICAL COTTON CALCULATIONS 

COUNTS OF TWISTED OR PLY AND CABLE 
YARNS. 

When single yarns are twisted together to 
form a ply yarn, the result is usually a heavier 
yarn than the counts divided by the number of 
ends twisted together, owing to the contraction 
in twisting. This can be proved by twisting two 
yarns together to a certain length, weighing 
them, and comparing the weight with the weight 
of single yarns of a similar length of the original 
counts. 

For calculation purposes, however, a cotton 
ply yarn composed of two or more yarns of equal 
counts is regarded as being the size of the single 
yarns divided by the number of strands; thus a 
yarn composed of two strands of 60 's twisted 
together is considered equal to one of 30's single; 
a yarn composed of three strands of 60 's is con- 
sidered equal to one of 20's single, but the more 
twist there is put into a yarn the more it will 
contract in length and the coarser will be the 
actual counts. 

Ply yarns which are composed of single 
strands of equal size of yarn are indicated by 
the number of strands which are twisted together 
and the counts of the single yarns written after- 
wards; thus 2/40 's means two yarns of 40 's 
twisted together, 3/100 's means three yarns of 
100 's twisted together. These yarns would be 
equal to single yarns composed of 20 's and 
33.33 's respectively. 

Cable yarns are composed of two or more ply 
yarns twisted together to form a fancy yarn. A 
4/2/50 's cable yarn would be composed of four 



PRACTICAL COTTON CALCULATIONS 25 

ends of 2/50 's twisted together, making in all 
eight ends of 50 's yarn, and would be equal to a 
single yarn of 6| counts. 

Unless used for fancy yarns for special pur- 
poses, two single yarns of unequal counts are sel- 
dom or never used, as equal single yarns com- 
bined make the best ply yarns. 

To Find the Counts of a Single Yarn Equal to a 
Ply Yarn Composed of 2 Single Yarns of Un- 
equal Counts. 

Rule 5. Divide the product of the two counts 
by their sum. 

Example. What counts of a single yarn is 
equal to a yarn composed of 30 's and 20's 
twisted together? 

3 X 20 600 10 , 

■30T2T = -55- = = 12floonntB,Aiw. 

To Find Counts of a Single Yarn Equal to a Ply 
Yarn Composed of 2 or more Yarns of Un- 
equal Counts. 
Rule 6. Divide the highest eon nix by itself 
and by each of the lower counts in succession; 
add results and divide into tin highest counts. 

Example. What would be equal in a single 
yarn to a ply yarn composed of 50 's, 80 's and 
100 'sf 



100 
100 
100 



100 = 1.00 
80 = 1.25 
50 = 2.00 



4.25 
100 -r- 4.25 = 23.53 's counts, Ans. 



26 PRACTICAL COTTON CALCULATIONS 

To Find Counts of a Yarn to Twist with a Given 
Yarn to Produce a Required Ply Yarn. 

Rule 7. Multiply the required counts by the 
given counts and divide by their difference. 

Example. What counts of yarn is required 
to twist with a 30 's to make a ply yarn equal to 
a 12 's? 

30 X 12 360 OA , . , 

— — = — — = 20 7 s counts, Ans. 

o\) — 1Z lo 

To Find Weight of Each Counts of Yarn Re- 
quired to Make a Given Weight of Ply Yarn 
when Yarns of Unequal Counts are Twisted 
Together. 
First, when only 2 counts are twisted together. 
Rule 8. Divide the highest counts by itself 
and by the other counts in succession. Add the 
quotients and divide into the total weight. 

The result will be the weight of the highest 
counts. 

Deduct the latter from the total weight to find 
the weight of the other counts. 

Example. It is desired to make 75 lbs. of 
ply yarn composed of 80 's and 60 's. What 
weight of each is required ? 

80 -5- 80 = 1 
80 -s- 60 = lVs 

¥k 

75 lbs. -*■ 2% = 32.14 lbs. of 80's, Ans. 

75 — 32.14 = 42.86 lbs. of 60's, Ans. 
If it is required to find the weight when more 
than two yarns are used the above rule will 
have to be modified. 



PRACTICAL COTTON CALCULATIONS Zt 

Example. It is required to make 100 lbs. of 
ply yarn composed of 100 's, 80 's and 50 's. 
What weight of each is required? 



100 
100 
100 



100 = 1 
80 = 1.25 
50 = 2 



4.25 
100 lbs. -r- 4.25 = 23.529 lbs. of 100 's, Ans. 
23.529 X 1.25 = 29.411 lbs. of 80's, Ans. 
23.529 X 2 =47.058 lbs. of 50 's, Ans. 



99.998 lbs. total weight. 

Rules 5 to 8 are only approximately correct 
because when yarns of unequal counts are 
twisted together, the coarser yarn has a tendency 
to retain a straight line and deflect the fine. yarn. 
For a given length of ply yarn it would there- 
fore be necessary to use a longer length of the 
fine than the coarse. 

Rules 5 to 8 will apply in all the systems, 
except spun silk, mentioned on page 20. 

To Find Weight of Each Kind of Warp Yarn Re- 
quired in a Group of Warps of Equal Length 
when Number of Ends of Each Kind, Counts, 
and Total Weight Are Known. 
Rule 9. Divide the number of ends of each 
counts by its own counts. Add quotients. The 
result is to the total weight as each quotient is to 
the weight required of the respective counts. 

Example. A set of warps are arranged as 
follows: 1st, 144 ends of 3/24 's; 2d, 88 ends of 
4/32's; 3d, 2400 ends of 50 's. What weight of 



28 



PRACTICAL (OTTOX < \W.< TLATIONS 



each Avarp is required to make a total weight of 
100 lbs., provided the warps are all the same 
length? 

144 ends of 3/24 's = 432 ends of 24 's 
88 ends of 4/32 's = 352 ends of 32 's 

432 ends -r- 24 's counts = 18 

352 ends -=- 32 's counts == 11 

2400 ends -~ 50 's counts = 48 



77 



77 


: 100 lbs. 


:18 


: 23.38 lbs. 


of 24 's, 


Ans. 


77 


: 100 lbs. 


:11 


: 14.28 lbs. 


of 32 's, 


Ans. 


77 


: 100 lbs. 


:48 


: 62.34 lbs. 


of 50 's, 


Ans. 



100.00 lbs. total weight. 



COUNTS OF SPUN SILK PLY YARNS. 

Spun silk is counted like cotton when in the 
single yarn, but when writing the counts of ply 
silk the first number indicates the actual counts ; 
thus 30/2, or 30 's 2 fold, means two strands of 
60 's. An equivalent to this in cotton would be 
written 2/60 's. 30/3, or 30 's 3 fold in spun 
silk means three strands of 90 's, whilst 3/30 's in 
cotton means three strands of 30 's. 

In some mills cotton ply yarn counts are 
written with the number of strands last, thus 
30 •), which means that it is equal to a 10 \s, but 
as this method conflicts with the silk method it 
is not as generally used as the method previously 
explained, i. e., writing the number of ply first. 



PRACTICAL COTTON CALCULATIONS 29 

TO FIND COUNTS, LENGTH OR WEIGHT OF 
COTTON YARN. 

To Find Counts of Cotton Yarn when Length and 
Weight Are Known. 

*Rule 10. Divide the length by the weight and 
by 840. 

Example. If 126000 yards of yarn weigh 
6 lbs. what are the counts .' 

126000 yards 

6 lbs. X 840 -25 s counts,^. 

To Find Length of Cotton Yarn when Counts and 
Weight Are Known. 

*Rule 11. Multiply fin counts by the ir<i<jhl 

and by Sit). 

Example. What length of yarn is contained 
in 6 lbs. of 25 's yarn? 

25 's counts X 6 lbs. X 840 = 126000 yds., Ans. 

To Find Weight of Cotton Yarn When Counts and 
Length Are Known. 

"Rule 12. Dividi the l< ngtli by the counts and 
by 840. 

Example. What is the weight of 126000 
yards of 25 's cotton yarn ! 

126000 vards 

= () Ins., Ans. 



25 'a counts X 840 





Weight in- lbs. 


are 


X 


equal - 


Counts 


to 


X ' 




840 



30 PRACTICAL COTTON CALCULATIONS 

The three preceding rules, 10, 11 and 12, may 
be summarized in — 

Formula A. To Find Counts, Length or Weight 
of Cotton Yarn when the Other Factors Are 
Known. 



Length in yards 



Rule. Divide the product of the remaining 
items of the group containing the required item 
into the product of the other group. 

TO FIND WEIGHT, COUNTS OK NUMBER OF 
HANKS OF YARN. 

To Find Weight of Yarn when Counts and Num- 
ber of Hanks Are Known. 
Rule 13. Divide the number of hanks by the 

counts. 

Example. What is the weight of 840 hanks 
of 110 's yarn? 

840 hanks -r- 110 's counts = 7.63 lbs., Ans. 

To Find Counts of Yarn when Weight and Num- 
ber of Hanks are Known. 

Rule 14. Divide the number of hanks by the 
'weight. 

Example. 260 hanks of cotton yarn weigh 
15 lbs. What are the counts? 

260 hanks — =— 15 lbs. = 17^ 's counts, Ans. 



PBACTICAL COTTON CALCULATIONS 31 

To Find Number of Hanks when Weight and 
Counts Are Known. 

Rule 15. Multiply the weight by the counts. 

Example. How many hanks are there in 
20 lbs. of 60 's yarn? 

20 lbs. X 60's counts = 1200 hanks, Ans. 

The three preceding rules, 13, 14 and 15, may 
be summarized in — 

Formula B. To Find Counts, Weight or Number 
of Hanks when the Other Factors Are 
Known. 

Counts are 

X \ equal j Number of hanks 

Weight in lbs. J to I 
Rule. Divide the product of the remaining 
items of tin group containing the required item 
into tlie product of the other group. 

For other data regarding yarns see "Twists 
Per Inch, Diameters and Breaking Weights." 

BEAM YARN AND WARP CALCULATIONS. 

It is intended in the following rules to cover 
as nearly as possible all calculations required for 
ascertaining the weight, counts, average counts, 
number of ends, length and number of hanks of 
warp yarns. 

To Find Counts of Yarn on a Beam when Length, 
Weight and Number of Ends Are Known. 
# Rule 16. Multiply the number of ends by 
the length and divide by 840 and the weight in 
pounds. 



32 PRACTICAL COTTON "CALCULATIONS 

Example. 1000 ends on a warp 1176 yards 
long weigh 40 lbs. What are the counts'? 

1000 ends X 1176 yards ^ 

840 X 40 lbs. 

Another method to find counts of yarn on a 
beam is as follows: Take off 120 ends each 
one yard long, or 240 ends each \ yard long, 
weigh them and divide the weight in grains into 
1000. There would be less liability to error if 
840 ends each one yard lonii' were taken and 
weighed, and the weight in grains divided into 
7000. 

This method is not as good as Rule 16 when 
the items dealt with there are known. 

To Find Weight of Yarn on a Beam when Length, 
Number of Ends and Counts Are Known. 

*Rule 17. Multiply the number of ends by 
the length and dividi by 840 and thi counts. 

Example. A warp 1176 yards long contains 
1000 ends of 35 's cotton yarn. What is the 
weight? 

1000 ends X 1176 yards JA „ ■ A 

OAr . w og , - - = 40 lbs., Ans. 

840 X : ^> s counts 

Rule 17 may be applied when desiring 

To Find Weight of Warp Yarn in a Piece of Cloth 

but it must be understood that the slashing 
length, not the cloth length, must be taken. 

The table on the following page indicates the 
number of yards of cotton yarn per pound, in 
counts ranging from 1 to 250. This will be 



PRACTICAL COTTON CALCULATIONS 



33 



found useful when dealing with problems in 
which the product of 840 and the counts, as in 
the preceding example, has to be considered. 



Cotton 


Yards per 


Cotton 


Yards per 


Cotton 


Yards per 


Counts. 


Pound. 


Counts. 


Pound. 


Counts. 


Pound. 


l 


840 


35 


29,400 


78 


65,520 


1% 


1,260 


36 


30,240 


79 


66,360 


2 


1,680 


37 


31,080 


80 


67,200 


2% 


2,100 


38 


31,920 


82 


68,880 


3 


2,520 


39 


32,760 


84 


70,560 


m 


2,940 


40 


33,600 


86 


72,240 


4 


3,360 


11 


34,440 


88 


73,920 


J'l- 


3,780 


42 


35,280 


90 


75,600 


5 


4,200 


13 


36,120 


92 


77,280 


5% 


4,(320 


41 


: 16, 960 


94 


78,960 


6 


5,040 


45 


37,800 


96 


80,640 


li'o 


5,460 


46 


38,640 


98 


82,320 


7 


5.880 


47 


39,480 


100 


84,000 


7'-> 


6,300 


48 


10,320 


105 


88,200 


8 ~ 


6,720 


19 


41,160 


110 


92,400 


8% 


7,140 


50 


42,000 


115 


96,600 


9 


7. 560 


51 


12,840 


120 


100,800 


'.•'•. 


7,980 


52 


43,680 


125 


105,000 


10 


S,ll)l) 


53 


14,520 


130 


109,200 


11 


9,240 


51 


45,360 


135 


113,400 


12 


10,080 


55 


16.200 


140 


117,600 


13 


10,920 


56 


17,040 


145 


121,800 


14 


11.76(1 


57 


47,880 


150 


126,000 


15 


12,600 


58 


18,720 


155 


130,200 


16 


13,440 


59 


19,560 


160 


134,400 


17 


14.280 


60 


50,400 


165 


138,600 


18 


15,120 


61 


51,240 


170 


1 12,800 


19 


15,960 


62 


52 080 


175 


147,000 


20 


16,800 


63 


52,920 


180 


151,200 


21 


17,640 


64 


5;;. 76i) 


185 


155,400 


22 


18,480 


65 


54,600 


190 


159,600 


23 


19,320 


66 


55,440 


195 


163,800 


24 


2(1,160 


67 


56,280 


200 


168,000 


25 


21,000 


68 


57,120 


21 15 


172,200 


26 


21,840 


69 


57,960 


210 


176,400 


27 


22,680 


70 


58,800 


215 


180,600 


28 


23,520 


71 


59,640 


220 


184,800 


29 


24,360 


72 


60, ISO 


225 


189,000 


30 


25,200 


7:'. 


61,320 


230 


193,200 


31 


26,040 


74 


62,160 


235 


197,400 


32 


26.8S0 


75 


63,000 


'J 10 


201,600 


33 


27,720 


76 


63,840 


245 


205,800 


34 


28,560 


77 


64,680 


250 


210, 



34 PRACTICAL COTTON CALCULATIONS 

FINDING WEIGHT OF YARN ON BEAMS IN 
THE LOOMS. 

When taking stock of the amount of yarn in 
the looms, it is customary for the overseer to 
figure the weight of a cut of yarn on each style 
made, by Rule 17. By ascertaining the number 
of cuts of yarn in the looms and multiplying by 
the weight per cut, the weight of yarn on the 
respective styles is obtained. 

Example. A style of goods is made with 
2400 ends of 60 's cotton yarn, 55 yards per cut 
(slashing length). It is required to find the 
weight of yarn per cut, and also for 20 cuts. 

By Rule 17— 

24 ol end L^ 55y ! -- 2.619 lbs. per cut, Ans. 
840 X 60 's counts L 

2.619 lbs. of yarn per cut X 20 cuts = 52.38 lbs., 

weight of 20 cuts, Ans. 

Some mills do not trouble to ascertain how 
many cuts of each style there are when taking 
stock, but assume each beam to be half full, and 
figure accordingly. This method, although per- 
haps serving the purpose, is not accurate unless 
the person who does the calculating accidentally 
guesses the total number of cuts of each style, 
which is not probable. 

To Find length of Yarn on a Beam when Counts, 
Weight and Number of Ends Are Known. 

*Rule 18. Multiply the counts by the weight 
and by 840, and divide by the number of ends. 



PRACTICAL COTTON CALCULATIONS 35 

Example. What is the length of a cotton 
warp of 1000 ends of 35 's yarn if the weight is 
40 pounds ? 

35 's counts X 40 lbs. X 840 .„_„ . . 

=1176 yds., Ans. 

1000 ends 



To Find Number of Ends on a Beam when Counts, 
Weight and Length Are Known. 

"Rule 19. Multiply the counts by the weight 
and by 840, and divide by the length. 

Example. What is the number of ends on a 
warp 1176 yards long, of 35 's yarn, if the weight 
is 40 lbs. ? 

35 's counts X 40 lbs. X 840 , .._ _ t 

r i„n y— - — 10()() en( H Ans - 

1176 yards 

The above rule is of a theoretical nature and 
will give only approximate results. 

The four preceding rules, 16 to 19, may be 
summarized in — 

Formula C. To Find Cotton Counts, Weight, 
Length or Number of Ends on a Beam. 







840 


er of ends 


are 




X 


- equal - 


Weight in pounds 


i in yards 


to 


X 


j 




, Counts of yarn 



Rule. Divide the product of the remaining 
factors of the group containing the required item 
into the product of the other group. 



36 PRACTICAL COTTON CALCULATIONS 

To Find Average Counts of Yarn in a Set of 
Warps Containing* Different Counts of Yarns. 

Rule 20. Divide the number of ends of single 
yarn of each counts by its own counts; add the 
>■< suits and divide into the total number of ends. 
Example. A warp pattern is arranged 5 ends 
of 20 's and 2 ends of 10 's. What are the average 
counts ? 

5 ends-=-20's = .25 
2 ends-h-10's=.2 

7 .45 

7 ends -=- .45 = 15.5 's average counts, Ans. 

It is advisable to find the total number of 
ends of each counts of yarn before proceeding as 
above. 

Example. A set of 3 warps contains 288 
ends of 3/20 % 136 ends of 4/28 's, and 2552 ends 
of 40 's. What are the average counts of the 
single yarns? 

288 X 3 = 864 single ends of 20 's 

136 X 4 = 544 single ends of 28 's 

864 ends -r- 20 's counts = 43.20 

544 ends -r- 28 's counts = 19.43 

2552 ends -=- 40's counts = 63.80 



3960 ends 126.43 

3960 total ends -^ 126.43 =31.32 's average 

counts, Ans. 
To Find Number of Ends in an Equally Reeded 
Warp when Sley and Width of Cloth Are 
Known. 
Rule 21. Multiply the sley by the cloth width 



PRACTICAL COTTON CALCULATIONS .",7 

and add the necessary number of ends for sel- 
vedges. 

Example. How many ends would there be 
in an 88 sley cloth, 32 inches wide, allowing 24 
ends extra for selvedges? 

88 sley X 32 inches = 2816 ends. 
2816 + 24 extra for selvedges = 2840 ends, Ans. 
The selvedges mentioned in the preceding 
example would consist of 48 ends. One half of 
these, 24 ends, are considered when multiplying 
the sley by the width. 

To Find Number of Hanks of Warp Yarn in a 
Piece of Cloth when Sley and Cloth Width 
Are Known. 

*Rule 22. Multiply sley by width; add sel- 
vedge ends; multiply answer by slashing length 
and divide by 840. 

Example. A cloth is made 32 inches wide, 
110 sley and 100 yards long, the take-up of the 
warp being 7%. How many hanks of warp are 
there in the cloth ? 
110 sley X 32 inches = 3520 + 32 for selvedges 

= 3552 ends in warp. 
100 yds. cloth + 7% = 107 yds. slashing length. 

3552 ends X 107 yards ACn AC , . e 

' — = 452.45 hanks of warp, 

840 Ans. 

To Find Number of Hanks in a Warp when Num- 
ber of Ends and Length Are Known. 

*Rule 23, Multiply the number of ends by the 
length, and divide by 840. 



38 PRACTICAL COTTON CALCULATIONS 

Example. How many hanks are there in a 
cotton warp 800 yards long, containing 1920 
ends? 

1920 ends X 800 yards ._ 9Qri 

nAri - — ■ = 1828.6 hanks, Ans. 

840 ' 

To Find Length of a Cotton Warp when Number 
of Hanks and Number of Ends Are Known. 

*Rule 24. Multiply the number of hanks by 
840, and divide by the number of ends. 

Example. What is the length of a warp of 
2000 ends that can be made with 350 hanks of 
cotton yarn ? 

350 hanks X 840 



2000 ends 



= 147 yards, Ans. 



To Find Number of Ends in a Warp with Any 
Unequally Reeded Pattern when Sley Reed, 
Width and Warp Layout Are Known. 

First find the number of full patterns by Rule 
26 and apply — 

Rule 25. Multiply the number of ends per 
pattern by the number of full patterns; add 
extra ends for any fraction of a pattern, accord- 
ing to warp layout; also add selvedge ends. 

Example. A fancy cloth is required to be 
32 inches wide and woven in a 90 sley reed. 
Allowing 64 ends in 16 dents for selvedges, how 
many ends will be required in the warp if the 
following warp layout is used? 



PRACTICAL 


COTTON CALCULATION 


JS 


Top Beam. 


Bottom Beam. 


Dei 


i/40's yarn 


50 's vara 






80 " 


40 


1 


6 


1 


1 


6 


1 
Skip 1 


1 


6 


1 


1 


6 


1 



39 



X 



6 ends 116 ends 48 dents 
By Kule 26 there are 29 full patterns and 
32 dents extra. 

116 ends 50 's X 29 patterns = 3364 ends 50 's 

6 ends 3/40 's X 29 patterns = 174 " 3/40 's 
32 extra dents X 2 ends per 

dent == 64 " 50 's 

64 ends for selvedges = 64 50 's 



3666 total ends 

Arts. 

If it is required to know the total number of 

ends of single yarn the 174 ends of 3/40 's would 

be figured as 522 single ends, making a total of 

4014 ends required in the warp. 

To Find Number of Patterns in an Unequally 
Reeded Cloth when Sley Reed, Width and 
Number of Dents per Pattern Are Known. 

Rule 26. Multiply one-half the sley reed by 
the width; deduct the number of dents for sel- 
vedges and divide by the number of dents per 
pattern. 

Example. A cloth is required to be 32 inches 
wide and woven in a 90 sley reed ; there are 48 



40 PRACTICAL COTTON CALCULATIONS 

dents per pattern. Allowing 16 dents for sel- 
vedges, how many patterns will there be? 

90 sley reed -=- 2 = 45 dents per inch. 

45 X 32 = 1440 total dents in warp. 

1440 — 16 dents for selvelges == 1424 dents. 

1424 dents on , , . 00 1 , 

= 29 patterns + 32 dents, 



48 dents per pattern 

Arts. 

To Find Percentage of Size on Warp Yarns. 

Rule 27. Deduct the weight of the yarn before 
sizing from the weight of the yarn after sizing; 
add two ciphers to the answer, or multiply by 
100, and divide by the weight of the unsized yarn. 

Example. A warp weighs 140 pounds after 
sizing and 130 pounds before sizing. What per- 
centage of size has been added ? 

140 — 130 = 10; 10X100 = 1000; 
1000 -$- 130 == 7.69 percentage of size, Ans. 

To Find Weight of Warp, in Ounces, per Yard of 
Cloth. 

*Rule 28. Divide the number of ends in the 
warp by 52.5 and the counts. 

(840 yards -f- 16 ozs. = 52.5) 

Example. A warp contains 3200 ends of 
60 's yarn. What is the weight per yard, in 
ounces? 

3200 ends 



52.5 X 60 's counts 



= 1.016 ozs., Ans- 



PRACTICAL COTTON CALCULATIONS 41 

WARP AND FILLING CALCULATIONS. 

After finding the number of yards per lb from 
a small piece of cloth it is sometimes necessary — 

To Find the Counts from the Weight of a Few 
Inches of Yarn. 

For this purpose use — 

*Rule 29. Multiply the number of incites of 
yarn that weigh 1 grain by .2314. (See con- 
stants. ) 

Example. 170 inches of yarn weigh 1 grain. 
What are the counts? 

170 inches X .2314 = 39.338 's counts, Ans. 

To Find Weight of Warp or Weight of Filling 
per Cut when Weight of Cut, % Warp or 
% of Filling Are Known. 

Rule 30. Multiply the weight of the cut by % 
warp to find the weight of the warp. 

Deduct the weight of the warp from the weight 
of the cut to find the weight of the filling. 

Example. A cut of cloth weighs 6 lbs. and 
contains 55% warp. What are the separate 
weights of warp and filling ? 

6 lbs. X -55 = 3.30 lbs. warp, Ans. 
6 lbs. — 3.30 = 2.70 lbs. filling, Ans. 



42 PRACTICAL COTTON CALCULATIONS 

Example No. 2. A cut of cloth weighs 8 
lbs. and contains 47% filling. What are the 
separate weights of filling and warp ? 

8 lbs. X .47 = 3.76 lbs. filling, Ans. 
8 lbs. — 3.76 = 4.24 lbs. warp, Ans. 

To Find Weight of Warp or Filling Required per 
Day When Number of Yards per Pound, Pro- 
duction and % of Warp Are Known. 

Rule 31. Divide the number of yards per day 
by the number of yards per lb. to find number of 
lbs. of cloth per day. 

Multiply the number of lbs. per day by the 
% of warp to find the weight of warp. 

Deduct the weight of the warp from the total 
weight to find the weight of the filling. 

This does not allow for waste, which must be 
added. 

Example. A cloth 6J yards per pound is 
produced from a loom at the rate of 39 yards per 
day. 55% of it is warp. What weight of warp 
and filling is required per day ? 

39 — 6^ = 6 lbs. of cloth per day. 

6 lbs. X .55 = 3.30 lbs. warp per day, Ans. 

6 lbs. — 3.30 = 2.70 lbs. filling per day, Ans. 



PRACTICAL COTTON CALCULATIONS 43 

FILLING CALCULATIONS. 

To Find Number of Hanks of Filling in a Piece 
of Cloth when Pick, Width in Reed and 
Cloth Length Are Known. 

*Rule 32. Multiply the pick by the width of 
the warp in the reed and the cloth length, and 
divide by 840. 

See tables on pages 81 and 82. 

Example. A cloth is made 100 X 120, 32 
inches wide and 50 yards long. How many 
hanks of filling does it contain ? 

By Rule 63 a 100 sley cloth 32 inches wide 
would be woven 34 inches wide in the reed. 

120 pick X 34 inches X 50 yards _._ D . . 
— ^j^r — - = 242.8 hanks 

y4U of filling, Am, 

To Find Length of Cloth that can be Woven with 
a Given Counts and Weight of Filling when 
Width in Reed and Pick Are Known. 

*Rule 33. Multiply the counts by 840 and 
the weight, and divide by the pick and the 
width of the warp in the reed. 

Example. 7.5 lbs. of 70 's filling is on hand 
to insert into a cloth to be woven 40 inches wide 
in the reed with 220 picks per inch. What 
length of cloth can be woven with it ? 

70 's counts X 840 X 7.5 lbs. rA11 , 

t^k — —, ^-. — P — = — — r- = 50.11 yards, 

220 picks X 40 inches in reed ^ 



44 PRACTICAL COTTON CALCULATIONS 

To Find Weight of Filling Required per Cut 
When Width in Reed, Pick, Cloth Length 
and Filling Counts Are Known. 

. ' :: Rule 34. Multiply width in reed in inches 
by pick and length of cloth in yards, and divide 
by 840 and the counts. 

If the weight in ounces is desired, multiply the 
result by 16. 

Example. A cloth is desired 56 yards long, 
with 220 picks of 70 's filling. The width in the 
reed is 40 inches. How many pounds of filling 
are required. 

40 inches X 220 picks X 56 yards Q qft , 

840 X 70 's filling counts - An*. 

When estimating the weight of filling required 
for stop peg checks, the average pick, not the 
ground pick, must be considered. 

To Find Weight of Each Separate Color of Fill- 
ing in Ginghams, Tartans and Similar Check 
Patterns. 

*Rule 35. Multiply the total weight of filling 
(see Rule 34) by the number of picks per pat- 
tern of the required color, and divide by the total 
number of picks per pattern. 

Example. Supposing the pattern of the 
filling in the preceding example contains 4 picks 
of twist, 16 picks of black and 24 picks of white, 
how many pounds of each color are required for 
each cut of cloth ? 



PRACTICAL COTTON CALCULATIONS 45 

4 + 16 + 24 = 44 picks per pattern. 
8.38 X 4 



44 

8.38 X 16 

44 
8.38 X 24 



44 



= .7618 pounds twist, Ans. 
— 3.0472 pounds black, Ans. 
= 4.5709 pounds white, Ans. 



Total, 8.3799 pounds. 

If the number of picks of each color, as in this 
example, bear a direct proportion to 1, and to 
each other, the problem may be simplified in the 
following manner : 4, 16 and 24 are in the same 
proportion as 1, 4 and 6. 

1 + 4+6=11 

8.38X1 - C1Q 

= ./618 pounds twist, Ans. 



11 

7618 X 4 = 3.0472 pounds black, Ans. 
7618 X 6 = 4.5708 pounds white, Ans. 



Total, 8.3798 pounds. 

To Find Weight of Each Separate Count or Kind 
of Filling" in Embossed Fabrics Such as 
Welts, Piques, Quilts, etc. 

*Rule 36. Multiply width in reed by pick, 
length of cloth in yards and number of picks of 
required counts per filling pattern, and divide by 
840, counts of filling, and number of picks in the 
filling pattern. 



46 PRACTICAL COTTON CALCULATIONS 

Example. If it is desired to weave a cut of 
Marseilles quilts, what weight of each kind of 
nlling will be required if the cloth is made to the 
following particulars: width in reed, 96 inches; 
pick, 162; cut length, 30 yards; filling pattern, 
2 picks of 10 's and 4 picks of 50 's alternately, 
6 picks completing the round? 

96 X 162 X30 X 2 



840 X 10 X 6 
96 X 162 X30 X 4 



= 18.5 lbs. of 10 's, Ans. 



= 7.4 lbs. of 50 's, Ans.. 



840 X 50 X 6 

To find counts of nlling required the following 
factors must be dealt with : number of yards per 
pound, cloth or cut length, slashing length of 
each warp used, warp counts., number of ends of 
each counts, % of size or dressing on warp 
yarns, picks per inch and width in reed, there- 
fore — 

To Find Counts of Filling Required in Any Cloth 
Use— 

*Rule 37. Divide the number of yards per cut 
by the number of yards per pound. 

This gives the weight of the cut in pounds. 

Multiply the number of ends of each counts by 
the slushing length per cut of the respective 
Warps and divide by 840 and the counts; add a 
certain % for size, if necessary. 

This gives the weight of the warp yarns. 

Deduct the weight of the warp from the weight 
of the cut. 

This gives the weight of the nlling. 



PRACTICAL COTTON CALCULATIONS 47 

Multiply the picks per inch by the width in the 
reed and the cloth length, and divide by 840 and 
the weight of the filling. 

Example. A cloth is required 76 X 80, 28 
inches wide, 12 yards per pound, with 60 's warp. 
Allow 3% for take-up and 4% for size on 
the warp. What counts of filling is required? 

Assume a certain length of cut, say 100 yards. 

100 yard cut -f- 12 yards per tb = 8.5 lbs., 

weight of cut. 
76 sley X 28 inches = 2128 ends + 32 for sel- 
vedges =2160 ends. 
100 yard cut + 3% = 103 yards, slashing length. 

2160 ends X 103 yards , AH ,. 

Q/<n x , CA , —, — — 4.41 lbs. warp. 

840 X 60's counts .17 = 4% size. 



4.58 lbs. warp and 
size ; this is considered warp. 

The preceding might have been done in one 
problem by adding the 4% for size to the slash- 
ing length, and using 107 instead of 103. 

8.5 lbs. weight of cut 
4.58 lbs. weight of warp 



3.92 lbs. weight of filling 
76 sley X 28 inches wide 



2 ends per dent, 

1064 dents 



1064 dents in reed. 



= 29.8 



35.71 dents per inch in a 76 sley reed i ncne s 

width in reed. 



48 PRACTICAL COTTON CALCULATIONS 

80 picks per in. X 29.8 in. X 100 yds. __ , 
840 X 3.92 lbs. filling filling 8 

required, Ans. 

If more than one warp counts is used, or more 
than one beam, each one must be considered 
separately. 

Cotton ply yarns are not usually sized. 



To Find Counts of Filling Required When Sley, 
Pick, Warp Counts and Average Counts Are 
Known. 

Rule 38. Divide the sum of the sley and pick 
by the average counts = A. 
Divide sley by warp counts = B. 
Deduct B from A = C. 
Divide pick by C = Ans. 

Example. A cloth is desired 96 X 100. The 
average counts necessary is 84.6 's and the warp 
counts on hand 74 's. What counts of filling 
must be used? 

96 sley + 100 pick = 196. 
196 -f- 84.6 average counts = 2.316 = A. 
96 sley -=- 74 warp counts = 1.297 = B. 
2.316 — 1.297 = 1.019 = C. 
100 pick -f- 1.019 = 98 's filling required, Ans. 

The above rule will also apply- 
To Find the Warp Counts 

if the filling counts are known, by substituting 
sley for pick, and filling for warp. 



PRACTICAL COTTON CALCULATIONS 49 

To Find Counts of Filling Required When Sley, 
Pick, Cloth Width, Warp Counts and Yards 
per Pound Are Known. 

*Rule 39. Divide 764 (see constants) by the 
cloth width and the number of yards per pound 
= A. 

Divide sley by warp counts = B. 

Deduct B from A = G. 

Divide pick by C = Ans. 

Example. A cloth is desired 96 X 100, 30 

inches wide, 11 yards per- It), the warp counts 

on hand are 74 's. What counts of filling is 
required ? 

76 4 _ = 2.315 = A. 

30 inches X 11 yards per lb. 
96 sley -f- 74 's warp counts == 1.297 = B. 
2.315 — 1.297 = 1.018 = C. 
100 pick -7- 1.018 = 98 's filling required, Ans. 

To Find Counts of Filling Required in a Cloth 
Containing 2 Different Counts of Filling 
Yarn, When Average Counts of Filling, 
Counts of 1 Filling, Number of Picks of Each 
Kind and Total Number of Picks per Pat- 
tern Are Known. 

Rule 40. Divide the total number of picks per 
pattern by the average counts of the filling = A. 

Divide the number of picks of the known 
counts of filling by the latter = B. 

Deduct B from A = C. 

Divide the number of picks of the required 
counts by C = Ans. 



50 PRACTICAL COTTON CALCULATIONS 

Example. A filling check pattern is arranged 
38 picks of coarse and 360 picks of fine filling. 
The average counts of the filling required is 46.6, 
and the counts of the coarse filling 15. 
What is the counts of fine filling required ? 

360 + 38 = 398 total picks. 
398 -*- 46.6 = 8.540 = A. 
38-7-15 = 2.533 = B. 



6.007 = C. 
360 -r- 6.007 = 60 's fine filling required, Ans. 

To Find Average Counts of Filling in a Cloth 
Containing 2 or more Counts of Filling. 

Rule 41. Divide the number of picks of each 
counts per pattern by its own counts; add the re- 
sults and divide into the total number of picks 
per pattern. 

Example. A cloth contains 38 picks of 15 's 
and 360 picks of 60 's filling in one pattern. 
What is the average counts of the filling? 

38 picks -r- 15 's counts = 2.533 
360 picks -r- 60 's counts = 6. 



398 8.533 

398 -f- 8.533 = 46.64 average counts, Ans. 



CLOTH CALCULATIONS. 



AVERAGE COUNTS OF YARN IN THE CLOTH. 

Cotton cloths are based on the number of 
yards per lb with a given width, sley and pick. 

It is customary, first, to find the average 
counts of yarn in the cloth and then to assume 
the counts of warp. 

In coarse grades of cloth the warp and filling 
are about equal, whilst in the finer grades the 
filling is considerably finer than the warp. 

In all average counts of yarn calculations the 
number of single yarns are considered; for 
example, 50 ends of 3/24 's would be considered 
150 ends of 24 's single, not 50 ends of 8's. 

To Find Average Counts of Yarn in a Piece of 
Cloth when Ends in Warp, Pick, Width in 
Reed and Number of Yards per Pound Are 
Known. 

Assume a certain length of cut and apply — 

*Rule 42. Divide length of cut by number of 
! lards per pound. 

This gives weight of cut. 

Multiply the number of ends by the slashing 
length. 

This gives length of warp, to which a certain 
must be added foi 
consider size as yarn. 



52 PRACTICAL COTTON CALCULATIONS 

Multiply the pick by the width in the reed and 
the cloth or cut length. 

This gives length of filling. 

Add length of warp to length of filling and 
divide by 840 and weight of cut = Ans. 

Example. A cloth contains 300 ends of 
2/20's, 200 ends of 4/28 's and 2400 ends of 40 's, 
80 picks per inch. It was woven 32 inches wide 
in reed, and weighs 4.52 yards per pound. 
Allow 20% for contraction on the 2/20's 
warp, 15% on the 4/28 's warp, and 10% for 
contraction and size on the 40 's warp. What 
are the average counts? 

Assume a 100 yard cut. 
100 yards cloth -f- 4.52 yards per Id = 22.12 lbs., 

weight of cut. 
300 ends of 2/20's = 600 ends. 
200 ends of 4/28 's = 800 ends. • 
2400 ends of 40 's = 2400 ends. 

600 ends X 120 yards = 72000 yards 20 's 

800 ends X 115 yards = 92000 yards 28 's 

2400 ends X HO yards = 264000 yards 40 's 

80 pick X 32 in. X 100 yds. = 256000 yds. filling 



684000 yds., total 
length of yarn. 

840^22.12^ = 36 ' 8 aV6rage C ° UntS ' Am - 

To Find Average Counts of Yarn in a Piece of 
Cloth when Sley, Pick, Width and Yards 
per Pound Are Known. 

*Rule 43. Add sley and pick together; multiply 



PRACTICAL COTTON CALCULATIONS 53 

result by width and yards per pound, and divide 
by 840. 

This rule does not make any allowance for size 
or contraction. (See Rule 44.) 

Example. A cloth is made 96 X 100, 30 
inches wide, and weighs 12 yards per lb. What 
are the average counts? 

100 + 96 = 196 

196 X 30 inches X 12 yards 

-oTTT-^ — - = 84 av. counts, 

840 Ans. 

To Find Average Counts of Yarn in a Cloth when 
Sley, Pick, Width and Number of Yards per 
Pound Are Known. 

*Rule 44. Multiply the sum of the sley and pick 
by the width and number of yards per pound, 
and divide by 764. (See constants.) 

This rule allows 10% for contraction and 
size. (See Rule 43.) 

Example. A cloth 96 X 220, 40 inches wide, 
weighs 3.6 yards per pound. What is the aver- 
age counts of the yarn ? 

96 sley + 220 pick = 316 

316 X 40 inches X 3.6 vards per lb 

-^fnr~ ~ = 59,5 av. 

counts, Ans. 

To Find Average Counts of Yarn in a Cloth when 
Sley, Pick and Counts of Warp and Filling 
Are Known. 

Rule 45. Divide sley by warp counts and 
pick by filling counts. Add results and divide 
into sum of sley and pick. 



54 PRACTICAL COTTON CALCULATIONS 

Example. A cloth 96 X 220 is made with 
45 's warp and 70 's filling. What is the average 
counts of the yarn ? 

96 sley -r- 45 's counts === 2.13 
220 pick -=- 70's counts = 3.14 



316 5.27 

316 -j- 5.27 = 60 's average counts, Arts. 

The preceding rules, 43, 44, 45, may be used — 

To Find Average Counts of Yarn in a Cloth when 
Only One Warp Counts is Used in a Cramped 
Stripe, 

by substituting ' ' average sley ' ' for ' ' sley. ' ' 

To Find Average Counts of Yarn in a Cloth Con- 
taining More than One Counts of Warp Yarn, 
when Width, Warp Counts, Number of Ends 
of Each Counts in Warps, Pick and Filling 
Counts Are Known. 

Rule 46. Multiply the pick by the cloth width 
= A. 

Divide A by the filling counts = B. 

Divide the number of ends of each counts by 
its own counts = G. 

Total number of ends — D. 

Divide sum of A and D by sum of B and C 
= Ans. 

Example. A cloth is made as follows: 80 
ends of 3/30 's, 2200 ends of 60 % 100 picks of 
75 's filling, 30 inches wide. What is the aver- 
age counts of the yarns? 

80 ends of 3/30 's = 240 ends of 30 's 



PRACTICAL COTTON CALCULATIONS 55 

100 picks X 30 inches = 3000 = A 

3000 -r- 75 = 40 = B 

240-f-30 = 8 =C 

2200-^-60 = 36.66 = 

240 + 2200 = 2440 = D 

3000 + 2440 = 5440 

40 + 8 + 36.66 = 84.66 

5440 -=- 84.66 = 64 average counts, Ans. 

Rule 46 assumes a normal contraction in 
length and width. If the cloth is a leno, lap- 
pet or any style where excessive rate of contrac- 
tion occurs on some ends, an allowance must be 
made for the same. For example, if it was 
necessary to allow say 140 yards of 3/30 's warp 
in the preceding example for 100 yards of cloth, 
i. e., to add 40%, the first part of C would be 
worked out as follows : 

240 -=- 30 = 8 ; 8 + 40% = 11.2 

The average counts in this case would of 
course be different from the answer to the pre- 
ceding example. 
Another rule dealing with the same factors is — 

Rule 47. Divide the average sley by the aver- 
age warp counts and the pick by the filling 
counts; add the results and divide into the sum 
of the average sley and the pick. 

The average sley may be found by Rule 51. 

The average warp counts may be found by 
Rule 20. 

Example. A cloth is made as follows: 80 
ends of 3/30 's, 2200 ends of 60 's, 100 picks of 
75 's filling, 30 inches wide. What is the average 
counts of the yarns ? 



56 PRACTICAL COTTON CALCULATIONS 

80 ends of 3/30 's = 240 ends of 30 's 

240 + 2200 = 2440 total ends 
2440 ends -=- 30 inches =-81.333 av. sley 
240 ends -f- 30 's counts = 8 
2200 ends -*- 60 's counts = 36.666 



2440 44.666 

2440 ends -^-44.666 = 54.6 's av. warp counts 

81.333 av. sley -=- 54.6 's av. warp = 1.489 
100 pick -=- 75 's filling =1.333 



181.333 2.822 

181.333 -f- 2.822 = 64 's average counts, Ans. 

To Find Average Counts of Yarn in a Cloth when 
% Warp, % Filling and Counts of Warp and 
Filling Are Known. 

Rule 48. Multiply the % warp by the warp 
counts and the % filling by the filling counts; 
add the products. 

Example. A cloth of which 54% of the 
material is warp and 46% filling is made with 
50 's warp and 60 's filling. What is the average 
counts of the yarn ? 

54% X 50 's warp counts = 27.00 
46% X 60 's filling counts = 27.60 



Average counts, 54.60's, Ans. 

Example. What is the average counts of 
the single yarns in a cloth in which 24% of the 
yarn is 3/20's warp, 14% is 4/28 's warp, 37% 
is 40 's warp, and 25% is 50 's filling? 



PRACTICAL COTTON CALCULATIONS 57 

24% X 20 's warp counts = 4.80 
14% X 28 's warp counts = 3.92 
37% X 40 's warp counts = 14.80 
25% X 50's filling counts = 12.50 

Average counts, 36.02, Ans. 

To Find Average Counts of Yarn from a Small 
Piece of Cloth. 

*Rule 49. Multiply the sum of the sley and 
pick by the number of square inches weighed and 
by 7000, and divide by the weight in grains, by 
36 and 764. (See constants.) 

In this rule 7000, 36 and 764 are constant 
factors— 

7000 



36 X 764 



= .254 



therefore the 36 and 764 can be dispensed with 
and .254 used instead of 7000, giving — 

*Rule 50. Multiply the sum of the sley and 
pick by the number of square inches weighed and 
by .254 and divide by the weight in grains. 

Example. 4 sq. inches of a piece of cloth 
96 X 220 weighs 5.4 grains. What are the 
average counts of the yarn ? 

96 + 220 = 316 

316 X4sq. in. X .254 '._ . 

— ^7- — = 59.45 av. counts, Ans. 

5.4 



58 PRACTICAL COTTON CALCULATIONS 

AVERAGE COUNTS OF CLOTH. 

To Find Average Sley when Number of Ends in 
Warp and Width of Cloth Are Known. 

Rule 51. Divide the number of ends by the 
width. 

Example. A cloth 32 inches wide contains 
2240 ends. What is the average sley? 

2240 ends -\- 32 in. = 70 average sley, Ans. 

In rinding average sleys, ply yarns are counted 
as the number of single yarns there are twisted 
together; 200 3-ply yarns would be counted as 
600 singles. 

Example. A cloth 28 inches wide contains 
2000 ends of single yarn and 36 ends of 4-ply 
cord yarn. What is the average sley? 

36 X 4 = 144 single strands in the 36-ply 
yarns. 

144 + 2000 = 2144 total ends. 
2144 ends -=- 28 in. = 76.57 average sley, Ans. 

To Find Average Sley in an Unequally Reeded 
Stripe when Actual Sley and Warp Layout 
Are Given. 

Rule 52. Multiply the number of ends per 
pattern by one half of the sley and divide by the 
number of dents per pattern. 

Example. The warp pattern in a piece of 
cloth contains 70 ends and occupies 16 dents of 
a 56 sley reed. What is the average sley ? 

70 ends X 28 (I of sley reed) = ^ ^ 

16 dents in one pattern ^ 5 



PRACTICAL COTTON CALCULATIONS 59 

To Find the Average Picks per Inch, when Check 
Pegs are Used, when Number of Pegs, Picks 
per Pattern, and Number of Ground Picks 
per Inch Are Known. 

Rule 53. Deduct the number of check pegs in 
one repeat of the pattern from the number of 
picks per pattern; divide the result into picks per 
pattern, and multiply by the picks per inch that 
the loom would put in if check pegs were not used- 

Example. A check pattern 196 picks per 
pattern, requiring 64 check pegs, is being woven 
with a pinion gear that would give 84 picks per 
inch if check pegs were not used. What is the 
average pick? 

196 picks per pattern — 64 check pegs = 132 
196 -r- 132 = 1.484 X 84 = 124.65 average pick, 

Ans. 

The above ride assumes 1 tooth to be taken up 
every pick. If a loom that takes up every 2 picks 
is used, multiply the number of check pegs by 2 
and proceed as above. 

To Find Average Picks per Inch, when Check 
Pegs are Used, when Number of Picks per 
Pattern and Size of Pattern Are Known. 

Rule 54. Divide the number of picks per pat- 
tern by the size of the pattern. 

Example. The filling pattern in a cloth 
measures If inches, and contains 160 picks. 
What is the average pick ? 

160 picks -f- 1.375 inches = 116 av. pick, Ans. 

When measuring the size of the pattern, it is 



60 PRACTICAL COTTON CALCULATIONS 

advisable to use a rule graded in tenths and 
twentieths of an inch. (See page 73.) 

Rule 54, substituting the word ends for picks, 
may be applied — 

To Find the Average Sley. 

In dealing with average pick when figuring 
production, every time the shuttle goes across is 
termed one pick, whether carrying single or ply 
yarns. It will be necessary to consider this only 
on box loom patterns. 



CALCULATIONS FOR CHECK PEG PATTERNS. 

See also "Average counts of cloths." 

To Find the Number of Ground Picks per Inch in 
a Cloth, when the Average Pick, Number of 
Teeth Used per Pattern, and the Number of 
Picks per Pattern Are Known. 

Rule 55. Multiply the average pick by the 
number of teeth used in one repeat of the pat- 
tern, and by 2 (if the loom takes up every 2 
picks), and divide by the picks per pattern. 

Example. A check pattern 196 picks to one 
repeat takes up 66 teeth, in a loom that takes 
up 1 tooth in 2 picks ; the average pick is 
124.65. What is the number of ground picks 
per inch? 

124.65 av. pick X 66 teeth X 2 

ing . , it - == 83.9 ground 

196 picks per pattern pickg per inchj 

Ans. 



PRACTICAL COTTON CALCULATIONS 61 

To Find Numbers of Check Pegs to Use per Pat- 
tern when Ground Pick, Average Pick and 
Size of Pattern Are Known. 

Rule 56. Deduct the ground pick from the 
average pick and multiply the result by the size 
of the pattern in inches. 

This rule assumes 1 tooth to 1 pick. If 1 
tooth is taken up every 2 picks, divide the result 
by 2. 

Example. A cloth is made with a pattern 
H inches; the ground pick is 84 and the aver- 
age pick 124. How many check pegs must be 
used per pattern, assuming 2 picks to 1 tooth ? 

124 average pick 
84 ground pick 

40 X 1.5 = 60; 60 -f- 2 = 30 pegs required, 

Ans. 

To Find Number of Check Pegs to Use in a Pat- 
tern when Ground Pick, Average Pick and 
Number of Picks per Pattern Are Known. 

Rule 57. Multiply the number of picks per 
pattern by the number of ground picks per inch 
and divide by the average pick. Deduct result 
from number of picks per pattern = Ans. 

This rule assumes 1 tooth to 1 pick. If 1 
tooth is taken up every 2 picks, divide result 
by 2. 

Example. A cloth is desired 98 average pick 
and 70 pick, assuming 1 tooth take-up to 1 pick. 
There are 40 picks per pattern? How many 
check pegs per pattern must be used? 



62 PRACTICAL COTTON CALCULATIONS 

40 picks per pattern X 70 ground pick 

98 average pick 

40 picks per pattern — 28.57 = 11.43, say 11 
teeth stopped, Ans. 

If the take-up in the above example had been 
2 picks to 1 tooth, 6 teeth per pattern would 
have to be stopped. 



CLOTH CONTRACTION. 

There are two things to be remembered when 
dealing with cloth calculations: 

First, the cloth is always shorter than the 
warp from which it was woven, due to the take- 
up by its being bent around the filling. 

Second, the cloth is always narrower than 
what the warp is spread in the reed. 

Although rules that have been proved prac- 
tical may be given to find the different items 
necessary for the reproduction of a piece of cloth, 
it must be understood that only approximate 
results can be obtained. 

The cloths from two looms working side by 
side may and do produce cloths that vary either 
in length or width, or both, under apparently 
the same conditions. 

If a correct percentage is not allowed for con- 
traction in width, two faults occur in the cloth : 

First, the cloth does not come out the desired 
width. 





PRACTICAL COTTON CALCULATIONS 63 

Second, the correct sley is not obtained. 

The following factors will modify to some 
extent the amount of contraction in length or 
width from warp to cloth. 

The Weave. The oftener the interlacings the 
more the shrinkage. For example, a plain cloth 



Fig. 1, 

JZZEBZBZ2BZ2ZSZ2ZZZZ 

Fig. 2. 

which interlaces as shown in Fig. 1 will require 
a longer warp than a 5 end warp sateen shown 
in Fig. 2 to produce a cloth of the same length, 
provided an equal number of picks per inch are 
used in each. The circles in Figs. 1 and 2 
represent picks. 

If some ends weaving a sateen stripe were run 
from the same beam as other ends weaving plain, 
all being reeded 2 in a dent, the ends weaving 
plain would take up faster than the sateen por- 
tion and either break by an excess of tension or 
pause the sateen ends to weave slack and be 
broken by the shuttle, but if the sateen was 
reeded 4 or 5 in a dent and the plain 2 in a 
dent the take-up would be about equal. 

The finer the quality and the softer the filling 
as compared with the warp the more will be the 
shrinkage in width. 



64 PRACTICAL COTTON CALCULATIONS 

If the filling is hard twisted and of a coarse 
nature, or coarser than the warp, the cloth will 
not shrink much in width. 

The more tension on the warp yarns the longer 
will be the cloth and the narrower the width, up 
to a certain limit. 

The difference in weather, system of sizing, 
class of loom used, tension on filling yarns, or 
sley and pick as compared with each other also 
varies the amount of shrinkage. 

The yarns in weaves of the cord type, where 
several ends or picks work together, act like 
coarse yarns and tend to retain a straight line, 
the other yarns doing all the bending. 



CONTRACTION IN LENGTH FROM WARP TO 
CLOTH. 

To Find Approximate % of Contraction in Length 
from Warp to Cloth. 

Rule 58. Multiply the pick by 3.5 and divide 
by the counts of the filling. 

For clotlis woven with counts lower than 50's 
multiply by 4 instead of 3.5. 

Example. A plain cloth is made 100 X120 
with 80 's warp and 90 's filling. What would 
be the approximate % of contraction in length 
from warp to cloth? 

120 picks X 3.5 

= 4f % contraction, Ans. 



90 's filling 



PRACTICAL COTTON CALCULATIONS 65 

To Find Length of Warp Required for a Given 
Length of Cloth in Lenos, Lappets, Fancy 
Combinations, and all Cloths where Some 
Ends Take up Considerably Faster than 
Others. 

Rule 59. Measure a certain length of cloth 
= A. 

Unravel the ends required and measure them 
= B. 

Multiply the length of cloth desired by B and 
divide by A = Ans. 

Example. The yarns from a cloth 5 inches 
long measure 5 h inches. How many yards of 
warp would be required for a 50 yard cut of 
cloth ? 

5.5 in. X 50 yards 

— ^-. — — = 55 yards, Ans. 
5 m. 

Where there is considerable difference in the 
take-up of the ends in a cloth, two or more 
warp beams should be used. 



REED CALCULATIONS. 

The four following examples are given to illus- 
trate how the shrinkages in width vary in cloths 
of different structure. 

Sample No. 1. 62 sley X 32 pick, 90 's warp 
and 140 's filling, plain weave, 40 inches in the 
reed, gives 39 inches cloth. 

The reed width here is almost 3% more than 
the cloth width. The reason for this small con- 



66 PRACTICAL COTTON CALCULATIONS 

traction is on account of the small number of 
picks as compared to sley. 

Sample No. 2. 48 X 128, 3/40 's warp and 
48 's filling, 31^ inches in the reed gives 28 
inches cloth. 

The reed width here is over 11% more than 
the cloth width. This excessive contraction is 
caused by the large pick, as compared to sley. 

Sample No. 3. 64 X 40, 48 's warp and 15 's 
filling, 33 inches in the reed gives 32 inches 
cloth. 

The reed width here is 3-|% more than the 
cloth width. 

Sample No. 4. 88 X 50, 48 's warp and 2/15 's 
filling, 34 inches in the reed gives 33^ inch 
cloth. 

The reed width here is 1J%* more than the 
cloth width. 

The small contraction in Samples 3 and 4 is 
caused by the light pick and heavy filling. 

The samples just noted are unusual structures 
of cloth, and are only mentioned to show how 
the contraction in width varies in amount. 

The following rules relating to contraction in 
width are approximately correct, for cloths 
where the sley and pick, and warp and filling, 
are nearly equal. 

It is usually understood when dealing with 
reed and sley calculations that 2 ends in each 
dent are intended, unless otherwise stated. 

For certain reasons cloths are sometimes 
woven with only one end in a dent; at other 
times they are woven 3 or more ends in a dent. 



PRACTICAL COTTON CALCULATIONS 



67 



To Find Number of Dents per Inch in Reed to 
Produce a Given Sley. 

Rule 60. Deduct 1 from the sley and divide 
by one of the following numbers: 



Ends per dent in reed. 


Divide by number 


1 


1.05 


2 


2.1 


3 


3.15 


4 


4.2 



Example. Find the number of dents per 
inch in the reed to give a 100 sley cloth by hav- 
ing 1, 2, 3 or 4 ends per dent. 



hnds per 
dent 




in reed. Sley. 




1 100—1: 


= 99 


2 100 — 1 


= 99 


3 100 — 1 


= 99 


4 100 — 1 : 


= 99 



Constant Dents per in. 
divisor. in reed. 

99 -r- 1.05 = 94.28 Ans. 
99 -f- 2.1 = 47.14 Ans. 
99 -r- 3.15 = 31.43 Ans. 
99-^4.2 =23.57 Ans. 



See table on the following page. 



68 PRACTICAL COTTON CALCULATIONS 

Table showing number of dents per inch in 
the reed to produce any even numbered sley 
from 48 to 132. 





DENTS PER INCH IN REED 


SLEY 


1 End per 


2 Ends pep 


3 Ends per 


4 Ends per 




Dent 


Df.nt 


Dent 


Dent 


48 


44.76 


22.38 


14.92 


11.19 


50 


46.66 


23.33 


15.55 


11.66 


52 


48.56 


24 .28 


16.19 


12.14 


54 


50 48 


25.24 


1(5 83 


12.62 


56 


52.38 


26.19 


17.46 


18.09 


58 


54.28 


27.14 


18.09 


13.57 


60 


56.18 


28.09 


18.73 


14.04 


62 


5S.10 


29 0--. 


19.03 


14.52 


64 


60.00 


30.00 


20.00 


K. 00 


66 


61.90 


30.95 


20.63 


15.47 


68 


63.82 


31 .91 


21 .27 


L5.95 


70 


65.72 


32 86 


21 91 


L6.43 


72 


67.64 


33.82 


22.55 


16.91 


• 74 


69.52 


34.76 


23.17 


17.38 


76 


71.42 


35.71 


23.81 


L7.85 


78 


7:1.32 


36.66 


24.44 


18.33 


80 


7.'.. 21 


37.62 


2."). os 


18.81 


82 


77.18 


38.59 


25.73 


19.29 


si 


79.04 


39.52 


26.35 


19.76 


86 


80.9(3 


10.48 


26.99 


20.24 


88 


82.86 


41.43 


27.65 


20.71 


90 


84.76 


12.38 


28.25 


21.19 


92 


sc. us 


13.34 


28.89 


21 .67 


94 


88.58 


44.29 


29.53 


22.14 


96 


90.50 


45.25 


30.17 


22 02 


98 


92.40 


46.20 


30.80 


23.10 


100 


94.28 


47.14 


31.43 


23.57 


102 


96.20 


48.10 


32.07 


24.05 


104 


98.12 


49.06 


32.91 


24.53 


106 


100.00 


50.00 


33.33 


25.00 


108 


101.90 


50.95 


33.97 


25.47 


110 


103.80 


51.90 


34.60 


25.95 


112 


105.72 


52.86 


35.24 


26.43 


114 


107.62 


53.81 


35.87 


26.90 


116 


109.52 


54.76 


36.51 


27.38 


118 


111.42 


55.71 


37.14 


27.85 


120 


113.32 


56.66 


37.77 


28.33 


122 


115.24 


57.62 


38.41 


28.81 


124 


117.14 


58.57 


39 05 


29.28 


126 


119.04 


59.52 


39.68 


29.76 


128 


120.95 


60.47 


40.32 


30.24 


130 


122.85 


61.43 


40.95 


30.71 


132 


124.76 


62.38 


41.59 


31.19 



PRACTICAL COTTON CALCULATIONS 69 

There are various methods of marking reeds 
adopted in the cotton trade, three of which are 
as follows: 1st — By indicating the total dents 
on a certain number of inches. 2nd — By 
marking the sley on the side of the reed. 
3rd — By marking the number of dents 
per inch. Sometimes reeds are marked 
by combinations of the above methods. 
If the number of dents on a certain number of 
inches are known, it is only necessary to divide 
the total dents by the number of inches to find 
the number of dents per inch. 

To Find Sley that would be Woven with a Reed 
of a Given Number of Dents per Inch. 

Rule 61. Multiply the number of dents per 
inch by one of the following numbers and add 
one: 
Ends per dent in reed. Multiply by number. 

1 1.05 

2 2.1 

3 3.15 

4 4.2 
Example, What sley cloth would be woven 

with a reed containing 40 dents per inch, with 
2 ends per dent? 

40 dents X 2.1 ==84 
84 + 1 = 85 sley cloth, Ans. 

To Find Sley Reed to Use for Unequally Reeded 
Patterns such as Bedford Cords, Lenos, Dimi- 
ties, Stripes, etc. 

Rule 62. Multiply the desired average sley by 
the number of dents per pattern and by 2, and 
divide by the number of ends per pattern. 



70 PRACTICAL COTTON CALCULATIONS 

Example No. 1. A warp pattern in a piece 
of cloth is found to be reeded 2 ends in 1 dent, 
12 ends in 3 dents, and there are 8 patterns in 
1 inch. What sley reed should be used to repro- 
duce it? 

14 ends per pattern X 8 patterns per inch 

= 112 average sley. 

112 X 4 dents per patt. X 2 _, _ 

— =-: ^ — — =64 sley reed, Ans. 

14 ends per patt. 

Example No. 2. It is desired to make a cloth 
125 average sley, with the warp reeded 64 
single ends in 32 dents; 4 singles and a 3-ply 
yarn in 1 dent, 2 empty dents, 4 singles and a 
3-ply yarn in 1 dent. What sley reed should be 
used? 

3-ply yarns count as 3 singles in considering 
the average sley. 
125 av. sley X 35 dents per patt. X 2 __ 1 1 _ , 

"Trends per patt. 7 eed ~ |^ 

To Find Width of Warp at the Reed when Width 
of Cloth and Sley Are Known. 

Rule 63. Multiply the width of the cloth by 
the sley and divide by the number of dents per 
inch in the reed and the number of ends per dent. 

See reed table on page 68. 

Example. It is desired to weave an 88 sley 
cloth 32 inches wide. How wide should the 
warp be spread in the reed ? 

An 88 sley cloth, 2 ends per dent, would be 
woven in a reed with 41.43 dents per inch. 

• 32 inches X 88 sley 00 no . 

Cl — . — £ — — 33.98 in., say 

41.43 dents per m. in reed X ^ 34 in Ans 



PRACTICAL COTTON CALCULATIONS 71 

To Find Number of Dents Occupied by an Equally- 
Reeded Warp. 

Rule 64. Divide the number of ends, less sel- 
vedges, by the number of ends per dent and add 
the necessary number of dents for selvedges. 

Example. How many dents would be re- 
quired for a warp of 2840 ends, 2 ends per dent, 
allowing 48 ends in 12 dents for selvedges-? 

2840 ends — 48 for selvedges = 2792 ends 

2792 -f- 2 = 1396 dents 

1396 dents + 12 for selvedges = 1408 dents. 



CLOTH ANALYSIS. 

For the convenience of those persons whose 
duty it is to analyze fancy cotton fabrics the 
figure at the top of page 73, which represents 
a 2-inch rule graded in lOths and 20ths, as well 
as the table on the same page, have been 
inserted. 

As previously stated in this book, it is advis- 
able to measure the various sections with a rule 
graded in lOths and 20ths of an inch because 
there are less figures than when using other 
divisions of an inch. 

A small pair of dividers should be used, when 
analyzing fabrics, to measure the various sec- 
tions successively. 

If the sample is to be duplicated in a different 
sle} r , the dents in the required sley for -any width 
of cloth from 1/20 inch to 1 inch may be seen in 
the table on page 73. 



72 



PRACTICAL COTTON CALCULATIONS 

ABC 



I) 



e:; 
m 



~ % M 



Fig. 1. 



For example, suppose it is desired to make a 
pattern like Fig. 1, in an 80 sley reed the pro- 
cedure will be as follows : 

First — Measure section A, and ascertain how 
many dents are necessary. A, in Fig. 1, meas- 
ures 16/20 of an inch. This width of an 80 
sley would require 32 dents. 

Second — Measure each denning part of the 
pattern separately and ascertain from the table 
how many dents each section requires. B = 
19/20 of an inch = 38 dents. C = 16/20 of an 
inch = 32 dents. D = 6/20 of an inch = 12 
dents. 

Third — Measure one complete pattern and 
ascertain how many dents are required. One 
pattern in Fig. 1 = 2 17/20 inches = 114 dents. 

The reason for measuring the full pattern is 
to prove that the various small sections are cor- 
rect. The sum total of the dents in each small 
section in one pattern should be similar to that 
obtained by measuring a complete pattern. 
There is a -great liability to error when measur- 
ing several small sections, but it is necessary 
that each section should be measured separately. 



PRACTICAL COTTON CALCULATIONS 



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74 PRACTICAL COTTON CALCULATIONS 

WEIGHT, OR NUMBER OF YARDS OF CLOTH 
PER POUND, AND OUNCES PER YARD. 

To Find Number of Ounces per Yard or Yards per 
Pound. 

Rule 65. itf-r- number of ounces per yard 
— - number of yards per pound. 

16 -=- number of yards per pound = number 
of ounces per yard. 

To Find Number of Yards of Cloth per Pound 
from a Small Portion of Cloth when Analyz- 
ing" Fabrics. 
Rule 66. Multiply the number of square inches 
weighed by 7000 grains and divide by the weight 
in grains, width of cloth in inches, and by 36. 

Example. A cloth is 18.5 inches wide; 6 
square inches weigh 8 grains. How many yards 
are there per pound? 

7000 grains X 6 inches 

5 : vy io g - — T. — w oa = '- ,ss > yards per 

8 grains X 18.5 inches X 36 ^ Ans ^ 

In Rule 66, 7000 and 36 are constant factors. 
7000 — 36 = 194.44, therefore instead of the 
above rule use the following: 

For 1 square inch -r- 194.44 by weight in 
grains and cloth width. 

For 4 square inches -=- 777.77 by weight in 
grains and cloth width. 

For 9 square inches -f- 1750 by weight in 
grains and cloth width. 

For 12 square inches -r- 2333.33 by weight in 
grains and cloth width. 

For cloth cut to any other size use Rule 67. 



PRACTICAL COTTON CALCULATIONS 75 

To Find Number of Yards per Pound of a Cloth 
Containing" Different Counts of Yarns, or Pat- 
terns that are Unequally Reeded; 
it is necessary to cut a piece of cloth containing 
only full patterns before weighing* and proceed- 
ing by- 
Rule 67. Multiply 194.41 by the number of 
square indies weighed, and divide by the weight 
in grains and the widtli of the cloth in indies. 

Example. A stripe pattern is reeded 2 ends 
in a dent for 40 ends and 4 ends in a dent for 20 
ends; the complete pattern in the cloth measur- 
ing f of an inch. A piece 3 inches warpway, 
i. e., lengthway, and 5 patterns fillingway weighs 
6 grains. The width of the cloth desired is 28 - 
inches. How many yards per pound will the 
cloth weigh? 

5 patterns X f inches per pattern = 3^ inches 
3 J X 3 = 9} square inches weighed 

194.44 X 9.375 inches 

— : . — = 10.8o yards per lb , 

6 grains X 28 inches , 

It is advisable to cut a certain number of pat- 
terns on a certain number of inches, if possible, 
to avoid fractions. 

To Find Number of Yards of Cloth per Pound 
when 2 or More Warps are Used, when 
Counts and Number of Ends on Each Warp, 
Contraction of and Size on Each Warp, Width 
in Reed, Pick and Counts of Filling Are 
Known. 
Assume a certain length of cloth, say 100 

yards, and use — 



76 PRACTICAL COTTON CALCULATIONS 

*Rule 68. Multiply the ends of each counts by 
the slashing length, and divide by 840 and the 
respective counts; add to this for size, if neces- 
sary. 

This gives weight of warp. 

Note. — When size is put on a warp, the con- 
traction and size are usually considered together 
when finding weight. 

Multiply the picks per inch by the width in reed 
and length of cut, and divide by 840 and the 
counts of the filling. 

This gives weight of filling. 
Add weight of warp and weight of filling 
together and divide into length of cut == Ans. 

Example. A cloth is required 28 inches 
wide, made with 100 ends of 3/24 ? s, 200 ends 
of 4/32 's, 2500 ends of 50 's and 84 picks per 
inch of 60 's filling. Allow 5% for contrac- 
tion on the 3/24 's warp, 45 % for contraction on 
the 4/32 's warp, and 10% for contraction and 
size on the 50 's warp. How many yards of 
cloth will there be per lb ? 

Assume a 100 yard cut. 

100 ends of 3/24 's= 300 ends of 24 's 

200 ends of 4/28 's = 800 ends of 28 's 

300 ends X 105 yds. slashing length „ r/> „ „ 

Q , A vy ;;,, - = 1.066 lbs. 

840 X 24 s counts f 3/24 's warp 

800 ends X 145 yds. slashing length r ,. 

840 X 32 's counts of ^33 > s ^ 

2500 ends X HO yds. slashing length r ^ ,, 

840 X 50 's counts \)F50's warp 



PRACTICAL COTTON CALCULATIONS 77 

For 28 inch cloth, say 30 inches in reed, 

84 picks per in. X 30 in. X 100 yds, cnt ^ „ 

840 X 60 's filling counts oFfiUing 

1.566 lbs. of 3/24 's warp 

4.315 lbs. of 4/32 's warp 

6.548 lbs. of 50 's warp 

5.000 lbs. of 60 's filling 



17.429 
100 yd. cut ^-17.429 lbs. = 5.738 yds. per lb, 

Ans. 

To Find Number of Yards of Cloth per Pound 
when Sley, Pick, Width and Average Counts 
Are Known. 

-Rule 69. Multiply the average counts by 761 
(see constants) and divide by the width and the 
sun) of sley and pick. 

Example. A cloth is made 96^X 150 and is 
334 inches wide ; the average counts is 58. How 
many yards of cloth are there in a pound? 

58 average counts X 764 _ 
96 -f- 150 X 33i inches " 5 ^ 77 3 ards per ^ 

To Find Number of Yards of Cloth per Pound 
when Sley; Pick, Width, Warp and Filling 
Counts Are Known. 

* Rule 70. Divide sley by warp counts = A. 
Divide pick by filling counts = B. 
Add A to B = G. 

Divide 764 (see constants) by C and the width 
=±= Ans. See Rule 71. 



78 PRACTICAL COTTON CALCULATIONS 

Example. A cloth is desired 64 X 124, 33^ 
inches wide, with 36 's warp and 48 's filling. 
How many yards will there be in a ponnd of 
cloth ? 

64 -=- 36 = 1.77 = A 

124 -4-48 = 2.58 ==B 

1.77 + 2.58 = 4.35 = 

4.35^33.515. = 5 " 24 yardS Per ft ' Am ' 

Another rule dealing with the factors men- 
tioned in the preceding example is as follows : 

*Rule 71. Divide the number of hank* for the 
sley and width given on the following table by 
the counts of the warp and the filling yarns; add 
both results together and allow for contraction 
a ad size, and divide into 100 {yards). 

Example. A cloth is made 28 inches, 72 X 68, 
with 80 's warp and 100 's filling; allow 10% for 
contraction and size. How many yards of cloth 
are there per pound? 

By examining the table 72 sley cloth, 28 inches 
wide contains 240 hanks of warp. A 68 pick 
cloth contains 226.66 hanks of filling for the 
same width. 

240 hanks warp -4- 80 's counts = 3 
226.66 hanks filling -4- 100 's counts = 2.266 



5.266 
add 10% .526 



Weight of 100 yards of cloth, 5.792 lbs. 
100 -f- 5.792 = 17.265 yards per lb, Ans. 



PRACTICAL COTTON CALCULATIONS 79 

*The tables on pages 80 and 81 will be found 
useful when finding the weight of warp or filling 
yarns in 100 yards of cloth. Allowance has not 
been made in this table for contraction or size, 
as these will vary in different classes of goods. 

The width in the reed instead of the width of 
the cloth should be considered in dealing with 
filling calculations. 

To Find Number of Ounces per Yard from a Small 
Piece of Cloth. 

Rule 72. Multiply the width of the cloth in 
inches by the weight of a small piece in grains 
and by 36, and divide by 437.5 (grs. per oz.) and 
the number of square inches weighed. 

Example. A piece of cloth 4 inches square 
weighs 16 grains. What is the weight in ozs. per 
yard of cloth 28 inches wide? 

28 inches X 16 grains X 36 

jT^rfr = rr-Tc : — x. — = 2 -3 ozs. per yd., 

437.5 grams X 16 sq. inches Ans 

In the above rule 36 and 437.5 are constant 
numbers, therefore the 36 above the line could 
be dispensed with and 12.152 used instead of 
437.5 below the line. (437.5 grs. per oz. -^ 36 
inches per yard — 12.152.) 

Using the preceding example the working 
would be as follows : 

28 inches X 16 grains 

101 r OV1c = — r — =2.3 ozs. per yd., Ans. 

12.152 X 16 sq. inches 



80 



PRACTICAL COTTON CALCULATIONS 



NUMBER OF HANKS OF YARN, WARP OR FILLING, 
IN 100 YARDS OF CLOTH. 

See note (*) on preceding page. 



r = ?J - z- * 



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PEACTICAL COTTON CALCULATIONS 



SI 



NUMBER OF HANKS OF YARN, WARP OR FILLING, 
IN 100 YARDS OF CLOTH. 

See note (*) on page 79. 



GO 

W 

b 

g 

i— i 

b 

r- 

c 

PH 
o 

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Q 


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445.72 

458.1 
470.48 
482.86 
495.25 

507.62 

520 

5:!2.:;s 

544.76 

557.14 

5(1! 1.52 

581 .91 

594.29 

606.66 

619.06 

631.45 

643.84 

65(1.21 

668.58 

(ISO. '.15 

693.33 

705.72 

718.1 

730.47 

742.SH 

755.25 

767.62 

780 

792.38 


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411.4 1 
422.86 
434.28 
4 15.71 
457.15 
468.57 

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491 .42 
502.84 
514.28 
525.72 
537.15 
548.57 
560 
571.11 
5S2.S6 
594.28 
(105.72 
617.16 
62S.5S 
640 

651 .43 
662.86 
674.28 
6S5.71 
697.15 
708.57 
720 
731.43 


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3.42. 84 

352.37 

361.90 

371.43 

380.95 

: 190. is 

loo 

109,52 

119.04 

428.56 

438.08 

147.61 

157.14 

466.66 

176.18 

185.73 

495.28 

504.77 

514.26 

52:!. 79 

533.33 

542.86 

552.38 

561.9 

571.43 

5S0.96 

590.47 

600 

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;;25.72 

334.77 

343.82 

352.86 

361.91 

370.96 

380 

3S9.04 

398.08 

407.13 

416.18 

425.24 

134.29 

443.33 

45-.'.: is 

461.43 

170. is 

479.53 

188.58 

497.62 

506.6(1 

515.72 

521.76 

533.8 

542.S6 

551.91 

560. 95 

540 

579.nl 


cc 


co -r oi ~ co cc cc o i x cc cc cc o i x -o -p o i i — p rH — cc :o i - 
.qt-Hi-oix-T iCr-i-:]-/. h icncrr/.r ,ff . r 1 l .*! y -. _ '"-. 

X 1 - ' O -p" CJ rH q x" 1 - ' — ' 0J rH = 30 1_; lO — ' Cj r-' - y' \J i Q — C i — i O / 


CO 


291.44 
29! 1.5:; 
307.62 
315.71 

323. SI 

331.9 

340 

348.08 

356.16 

364.26 

380'.47 

388.57 

396.66 

404.76 

412.84 

420.92 

429.04 

437.16 

445.24 

453.33 

161.43 

46! 1.52 

477.62 

185.71 

193.81 

501.9 

510 

518.09 


CO 


274.28 

281.9 

289.52 

297.14 

304.75 

312.38 

320 

327.62 

335.24 

342.86 

350.48 

358.10 

388.55 
396.16 
103 79 
111.42 
419.04 
426.66 
134.29 
441.9 
149.52 
157.11 
464.76 
172.38 

ISO 
187.61 


o 

CO 


C 1 1 - C 1 1 - — CC — X 1 CO r- CO — CC — CO X — -/. TII-h.C -r 

r- 1 c i — ; i q i - x r- c i — . q i - x r- ■ o i — i o q x r-:i-T,:i-. x r-j 
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.0 cc 1- 1- x re r — ci ci cc — ic 1.0 1- 1- / ~ — ~ r- 01 01 cc — • : .0 
01 ci ci ci 01 ci cc cc :c :c cc cc cc :: :c :c :c :c :c :: - — 


X 

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s^sisg§gssg8B88a5$^g||8|gggss|gg§g 


* 



82 PRACTICAL COTTON CALCULATIONS 

PERCENTAGE OF WARP OR FILLING. 

To Find % of Warp or Filling in Any Cloth. 

*Rule 73. Multiply the number of ends in 
each warp by the slashing length, and divide by 
840 and the counts. Add the results to obtain 
the weight of warps. 

Multiply the width in reed by the number of 
picks of each count of filling per inch and the 
cloth length, and divide by 840 and the counts. 
Add results for weight of filling. 

Add weight of warp and weight of filling to 
find weight of cut. 

Divide weight of each counts by the total 
iveight to find %. 

Example. An embossed quilt fabric is con- 
structed as follows: 7200 ends of 40 's yarn for 
face warp; 3600 ends of 20 's warp for stitching; 
60 's filling for face and back; 12 's filling for 
wadding; 160 picks per inch, arranged in the 
proportion of 3 fine to 1 wadding; 98 inches in 
the reed; slashing length of 40 's warp, 110 
yards; slashing length of 20 's warp, 105 yards; 
length of cut, 100 yards. What is the % of 
each count of yarn in the cloth? 

7200 ends X HO yards nn rr7 „ M AiX% 

Q , n ^ A( C ~ = 23.57 lbs. of 40 's warp. 

840 X 40 s counts ^ 

3600 ends X 105 yards rn 

Q/1A v/ OA , - = 22.50 lbs. of 20 's warp. 
840 X 20 's counts F 

Total weight of warp, 46.07 lbs. 

98 inches X 120 picks X 100 yard s _ 

840 X 60 's counts of "^ ' m - n * 



PRACTICAL COTTON CALCULATIONS 83 

98 inches X 40 picks X 100 yards _ ss 

840 X 12 's counts of wad 7 ing ' fining. 

Total weight of filling, = 62.21 lbs. 

23.57 
22.50 
23.33 

38.88 



108.28 lbs., weight of 100-yard cut of cloth. 

23.57 -5- 108.28 = .217, or 21.7%, 40's warp, 

Ayig 

22.50 -r- 108.28 = .207, or 20.7%, 20 's warp, 

23.33 -r- 108.28 = .215, or 21.5%, 60's filling, 

38.88 -v- 108.28 = .359, or 35.9%, 12 's filling, 

Ans. 
The % may be found without finding the 
weight, as in the preceding example, by dispens- 
ing with the 840 and dividing by the counts 
only. Using the preceding problem as an illus- 
tration : 

7200 X HO 



40 
3600 X 105 



= 19800 



20 
92 X 120 X 100 



= 18900 



60 
98 X 40 X 100 



= 19600 



12 



= 32666 



90966 



84 PRACTICAL COTTON CALCULATIONS 



19800 
18900 
19600 
32666 



90966 = .211, or 21.7%. 
90966 = .207, or 20.7%. 
90966 = .215, or 21.5%. 
90966 = .359, or 35.9%. 



Total, .998, or 99.8%. 



Rules to indicate the methods usually used 
for finding % of warp or filling in equally bal- 
anced cloths of one warp and one filling. Nor- 
mal contractions in length and width of cloth, 
one balancing the other, are assumed when these 
are applied. 



To Find % of Warp or Filling in a Piece of Cloth 
when Ends in Warp, Pick, Warp, Filling 
and Width of Cloth Are Known. 

Rule 74. Divide the number of ends in the 
warp by the warp counts = A. 

Multiply the pick by the width of the cloth, 
and divide by the filling counts = B. 

Divide A by sum of A and B for % warp 
= Ans. 

Divide B by sum of A and B for % filling 
= An s. 

Or deduct % warp from 100% for % filling 
= Ans. 

Example. A cloth 30 inches wide contains 
2160 ends of 60 's warp and 68 picks per inch of 
85 \s filling. What are the relative percentages 
of warp and filling? 



PRACTICAL COTTON CALCULATIONS 85 

2160 ends -±- 60 's counts = 36 = A 
68 picks X 30 inches 
85 filling counts 

36 + 24 = 60 
36 -^ 60 = .60 or 60% warp, Ans. 
100%,— 60%, = 40% filling, Ans. 

To Find % Warp or Filling when Weight of 
Warp and Weight of Cut Are Known. 

Rule 75. Divide weight of warp by weight of 
cut for % warp = Ans. 

Deduct '/< warp from 100% for % filling = 

Ans. 

Example. A cut of cloth weighing 8 lbs. 
contains 4.8 lbs. of warp. What are the rela- 
1 ive percentages of warp and filling? 

4.8 lbs. warp -f- by 8 lbs. cut = .60 or 60% 

warp, Ans- 
100%, — 60% == 40% filling, Ans. 

To Find % of Warp or Filling in a Piece of Cloth 
When Sley, Pick, Warp and Filling Counts 
Are Known. 

Rule 76. Divide the sley by the warp counts 
= A. 

Divide the pick by the filling counts ==B. 

Divide A by sum of A and B for % warp 
— Ans. 

Divide B by sum of A and B for % filling 
= Ans. 

Or deduct % warp from 100% for % filling 
= Ans. 



86 PRACTICAL COTTON CALCULATIONS 

Example. A cloth 72 X 68 is woven with 
60 's warp and 85 's filling. What are the rela- 
tive percentages of warp and filling? 

72 sley -f- 60 's counts warp = 1.2 = A 

68 pick ~i- 85 's counts filling = .8 = B 

1.2 + .8 = 2 

.8-^2= .40 or 40% filling, Ans. 

or 100 — 60 = .40 or 40% filling, Ans. 

To Find % Warp or Filling in a Piece of Cloth 
when Sley, Pick, Average Counts and Warp 
Counts Are Known. 

Rule 77. Add sley and pick together and 
divide by the average counts — A. 

Divide sley by warp counts = B. 

Divide B by A = % warp = Ans. 

Deduct % warp from 100% for % filling = 
Ans. 

Example. A cloth is made 104 X 112. The 
average number is 90 and the warp 80 's. What 
is the % warp? 

104 sley + 112 pick = 216 -f- 90 's average 
counts = 2.4 = A. 

104 sley -=- 80 's warp counts = 1.3 = B. 
1.3 -r- 2.4 = 54% warp, Ans. 

The preceding rule may be applied to find 
% filling by substituting the filling counts for 
the warp counts and dividing the pick by the 
filling counts to find B. 

Note. — If % warp or % filling is found it is 
only necessary to deduct same from 100% to 
find the % of the other. 



PRACTICAL COTTON CALCULATIONS 87 

To Find Number of Square Yards in a Piece of 
Cloth. 

Rule 78. Multiply inches in width by length 
in yards and by 36 (inches in a yard) and divide 
by 1,296 (square inches in a yard). 

Example. How many square yards are there 
in a piece of cloth 42 inches wide and 56 yards 
long ? 

42 inches X 56 yards X 36 inches _. 

1296 sq. ins. in a sq. yd. = ^ l Ans 

In the above rule, 36 inches to a yard, and 
1296 square inches to a square yard, are con- 
stant factors; by dividing 1296 by 36 the result 
is 36, which can be used as a constant, and the 
36 and 1296 dispensed with, giving — 

Rule 79. Multiply width in inches by length 
in yards and divide by 36. 

Using the preceding example the working 
would be as follows: 

42 inches X 56 yards nrA 

— wn~ —=65^ sq. yards, Ans. 



TWISTS PER INCH IN YARNS. 



The number of turns or twists per inch to put 
into yarns varies somewhat according to the 
quality of the material used and the use to which 
the yarn is to be subjected. 

The following list is copied from two of the 
leading textile journals of England, "The 
Textile Manufacturer" and "The Textile 
Recorder," and may be said to be the generally 
accepted standard of twists per inch in Eng- 
land : 

Hosiery, sq. root of counts of yarn X 2.5 to 
2.75. 

Filling (medium), sq. root of counts of yarn 
X 3.25. 

Filling (fine), sq. root of counts of yarn 
X 3.183. 

Warp (medium), sq. root of counts of yarn 
X 3.75. 

Warp (fine), sq. root of counts of yarn 
X 3.606. 

Warp (extra hard ring), sq. root of counts of 
yarn X 4. 

Warp (Sea Island stock), sq. root of counts 
of yarn X 4.75. 

The square roots of the counts, from 1 to 140, 
will be found in the tables on pages 90 and 91. 



PRACTICAL COTTON CALCULATIONS 89 

The following list shows the number of turns 
per inch that are generally accepted as standards 
in the United States : 

Hosiery, sq. root of counts of yarn X 2.75. 

Mule Filling, sq. root of counts of yarn X 3.25. 

Mule Warp, sq. root of counts of yarn X 3.75. 

Mule Warp (extra), sq. root of counts of 
yarn X 4.00. 

Ordinary Warps, sq. root of counts of yarn 
X 4.75. 

The preceding twist constants are practically 
used only for guidance. 

When a progressive mill management starts 
out to get a yarn suitable for a given purpose, 
it experiments and varies the amount of twist 
until a satisfactory result is obtained. 

Although warp yarn is usually twisted more 
than filling, there are some mills that do 
not use a constant greater than 3.25 for warp 
yarn. 



TWIST TABLE. 



On pages 90 and 91 will be found twist tables, 
used by permission of Draper Co., Hopedale, 
Mass. These show the square roots of all 
counts from 1 to 140, also the number of turns 
per inch for the last four kinds of yarns in the 
U. S. list. 



90 



PRACTICAL COTTON CALCULATIONS 



TWIST TABLE, 

Showing the square root of the numbers or counts from 1 to 140 hacks in the pound, 

with the twist per inch for diffeient kinds of yarn. 



Counts 
or 


Square 
Root 


Ordinary 
Warp 


Warp 


Extra 
Mule Warp 


Mule Warp 
Twist 


Mule 
Filling 


Numbers. 


Twist. 


Twist 


Twist. 


Twist. 


1 


1 .0000 


4.75 


4.SO 


4.00 


3.75 


3.85 


2 


1.4142 


6.72 


6.36 


6.66 


5.30 


4.60 


3 


1.7321 


8.23 


7.79 


6.93 


6.50 


5.63 


4 


2.0000 


9.50 


9.00 


8.00 


7.50 


6.50 


6 


2.2361 


10.62 


10.06 


8.94 


8.39 


7.27 


6 


2.4495 


11.64 


11.02 


9.80 


9.19 


7.96 


.7 


2.6458 


12.57 


11.91 


10.58 


9.92 


8.60 


8 


2.8284 


13.44 


12.73 


11.31 


10.61 


9.19 


9 


3.0000 


14.25 


13.50 


12.00 


11.25 


9.75 


g? 


3.1G23 


15.02 


14.23 


12.65 


11.80 


10.28 


3.3100 


15.75 


14.92 


13.27 


12.44 


10.78 


12 


3.4041 


16.45 


15.59 


13.80 


12.99 


11.26 


13 


3.0056 


17.13 


16.22 


14.42 


13.52 


11.72 


14 


3.7417 


17.77 


16.84 


14.97 


14.03 


12.16 


15 


3.8730 


18.40 


17.43 


15.49 


14.52 


12.69 


16 


4.0000 


19.00 


18.00 


16.00 


15.00 


13.00 


17 


4.1231 


19.58 


18.55 


10.49 


15.40 


1 3.40 


18 


4.2426 


20.15 


19.09 


10.97 


15.91 


13.79 


19 


4.3589 


20.70 


19.62 


17.44 


16.35 


14,17 


20 


4.4721 


21.24 


20.12 


17.89 


16.77 


14:53 


21 


4.5826 


21.77 


20.62 


18.33 


17.18 


14.89 


22 


4.6904 


22.28 


21.11 


18.76 


17.59 


15.24 


23 


4.7958 


22.78 


21.58 


19.18 


17.98 


15.59 


24 


4.8990 


23.27 


22.05 


19.60 


18.37 


15.92 


26 


5.0000 


23.75 


22.50 


20.00 


18.75 


16.25 


26 


5.0990 


24.22 


22.95 


20.40 


19.12 


16.57 


27 


5.1962 


24.68 


23.38 


20.78 


19.49 


16.89 


28 


5.2915 


25.13 


23.81 


21.17 


19.84 


17.20 


29 


5.3852 


25.58 


24.23 


21.54 


20.19 


17.50 


30 


5.4772 


20.02 


24.65 


21.91 


20.54 


17.80 


31 


5.5678 


20.45 


25.05 


22.27 


20.88 


18.10 


32 


6.6569 


20.87 


25.46 


22.63 


21.21 


18.38 


33 


5.7446 


27.29 


25.85 


22.98 


21.54 


18.67 


34 


5.8310 


27.70 


26.24 


23.32 


21.87 


18.95 


36 


5.9161 


28.10 


26.62 


23.66 


22.19 


19.23 


36 


6.0000 


28.50 


27.00 


24.00 


22.50 


19.50 


37 


6.0828 


28.89 


27.37 


24.33 


22.81 


19.77 


38 


6.1644 


29.28 


27.74 


24.66 


23.12 


20.03 


39 


6.2450 


29.06 


28.10 


24.98 


23.42 


20.30 


40 


6.3240 


30.04 


28.46 


25.30 


23.72 


20.55 


41 


6.4031 


30.41 


28.81 


25.61 


24.01 


20.81 


42 


6.4807 


30.78 


29.16 


25.92 


24.30 


21.00 


4? 


6.5574 


31.15 


29.51 


26.23 


24.59 


21.31 


44 


6.6332 


31.51 


29.85 


26.53 


24.87 


21.56 


45 


6.7082 


31.80 


30.19 


26.83 


25.16 


21.80 


46 


6.7823 


32.22 


30.52 


27.13 


25.43 


22.04 


47 


0.8557 


32.60 


30.85 


27.42 


25.71 


22.28 


48 


6.9282 


32.91 


31.18 


27.71 


25.98 


22.52 


49 


7.0000 


33.25 


31.50 


28.00 


26.25 


22.75 


no 


7.0711 


33.59 


31.82 


28.28 


26.52 


22.98 


5J 


7.1414 


33.92 


32.14 


28.57 


20.78 


23.21 


.-.2 


7.2111 


34.25 


32.45 


28.85 


27.04 


23.44 


53 


7.2801 


34.58 


32.76 


29.12 


27.30 


23.66 


54 


7.3485 


34.91 


33.07 


29.39 


27.56 


23.88 


66 


7.4162 


35.23 


33.37 


29.00 


27.81 


24.10 


56 


7.4833 


35.55 


33.67 


29.93 


28.06 


24.32 


67 


7.6498 


35.86 


33.97 


30.20 


28.31 


24.54 


58 


7.6158 


36.17 


34.27 


30.46 


28.56 


24.75 


59 


7.6811 


36.49 


34.57 


30.72 


28.80 


24.96 


60 


7.7460 


36.79 


34.86 


30.98 


29.06 


25.17 


61 


7.8102 


37.10 


35.15 


31.24 


29.29 


25.38 


62 


7.8740 


37.40 


35.43 


31.60 


29.63 


25.59 


63 


7.9373 


37.70 


35.72 


31.75 


29.76 


25.80 


64 


8.0000 


38.00 


36.00 


32.00 


30.00 


26.00 


66 


8.0623 


38.30 


36.28 


32.25 


30.23 


26.20 


66 


8.1240 


38.59 


36.56 


32.50 


30.47 


26.40 


67 


8.1854 


38.88 


36.83 


32.74 


30.70 


26.60 


68 


8.2462 


39.17 


37.11 


32.98 


30.92 


26.80 


69 


8.3066 


39.46 


37.38 


33.23 


31.15 


27.00 


70 


8.3666 


39.74 


37.66 


33.47 


31.37 


27.19 



PRACTICAL COTTON CALCULATIONS 



91 







TWIST 


TABLE. Continued. 






Counts 

OT 


Square 
Root. 


Ordinary 
Warp 


Warp 


Extra 
Mule Warp 


Mule Warp 
Twist 


Mule 
Filling 


Numbers. 


Twist. 


Twist 


Twist. 


Twijt. 


1 


1.0000 


4.7P 


4.50 


4.0O 


3.75 


3.25 


71 


8.4261 


40.02 


37.92 


33.70 


31.60 


27.38 


72 


8.4853 


40.31 


38.18 


33.94 


31.82 


27.58 


73 


8.5440 


40.58 


38.45 


34.18 


32.04 


27.77 


74 


8.6023 


40.86 


38.71 


34.41 


32.26 


27.96 


75 


8.6603 


41.14 


38.97 


34.64 


32.48 


28.15 


76 


8.7178 


41.41 


39.23 


34.87 


32.69 


28.33 


77 


8.7750 


41.68 


39.49 


35.10 


32.91 


28.52 


78 


8.8318 


41.95 


39.74 


35.33 


33.12 


28.70 


79 


8.8882 


42.22 


40.00 


35.55 


33.33 


28.89 


80 


8.9443 


42.49 


40.25 


36.78 


33.54 


29.07 


81 


9.0000 


42.75 


40.50 


36.00 


33.75 


29.25 


82 


9.0554 


43.01 


40.75 


36.22 


33.96 


29.43 


83 


9.1104 


43.27 


41.00 


36.44 


34.16 


29.61 


84 


9.1652 


43.53 


41.24 


36.66 


34.37 


29.79 


85 


9.2-195 


43.79 


41.49 


36.88 


34.57 


29.96 


86 


9.2736 


44.05 


41.73 


37.09 


34.78 


30.14 


87 


9.3274 


44.31 


41.97 


37.31 


34.98 


30.31 


88 


9.3808 • 


44.56 


42.21 


37.52 


35.18 


30.49 


89 


9.4340 


44.81 


42.45 


37.74 


35.38 


30.66 


90 


9.4868 


45.06 


42.69 


37.95 


35.58 


30.83 


91 


9.5394 


45.31 


42.93 


38.16 


35.77 


31.00 


92 


9.5917 


45.56 


43.16 


38.37 


35.97 


31.17 


93 


9.6437 


45.81 


43.40 


38.57 


36.16 


31.34 


94 


9.6954 


46.05 


43.63 


38.78 


36.36 


31.51 


95 


9.7468 


46.30 


43.86 


38.99 


36.55 


31.(58 


96 


9.7980 


46.64 


44.09 


39.19 


36.74 


31.84 


97 


9.8489 


46.78 


44.32 


39.40 


36.93 


32.01 


98 


9.8995 


47.02 


44.55 


39.60 


37.12 


32.17 


99 


9.9499 


47.26 


44.77 


39.80 


37.31 


32.34 


lOO 


10.0000 


47.50 


45.00 


40.00 


37.50 


32.50 


101 


10.0499 


47.74 


45.22 


40.20 


37.69 


32.66 


102 


10.0995 


47.97 


45.45 


40.40 


37.87 


32.82 


103 


10.1489 


48.21 


45.67 


40.60 


38.06 


32.98 


104 


10.1980 


48.44 


45.89 


40.79 


38.24 


33.14 


105 


10.2470 


48.67 


46.11 


40.99 


38.43 


33.30 


106 


10.2956 


48.90 


46.33 


41.18 


38.61 


33.46 


107 


10.3441 


49.13 


46.55 


41.38 


38.79 


33.62 


108 


10.3973 


49.36 


46.77 
46.98 


41.57 


38.97 


33.77 


109 


10.4403 


49.59 


41.76 


39.16 


33.93 


110 


10.4881 


49.82 


47.20 


41.95 


39.33 


34.09 


111 


10.5357 


50.04 


47.41 


42.14 


39.51 


34.24 


112 


10.5830 


50.27 


47.62 


42.33 


39.69 


34.39 


113 


10.6301 


50.49 


47.84 


42.52 


39.86 


34.55 


114 


10.6771 


50.72 


48.05 


42.71 


40.04 


34.70 


115 


10.7238 


50.94 


48.26 


42.90 


40.21 


34.85 


116 


10.7703 


51.16 


48.47 


43.08 


40.39 


35.00 


117 


10.8167 


51.38 


48.67 


43.27 


40.56 


35.15 


118 


10.8628 


51.60 


48.88 


43.45 


40.74 


35.30 


119 


10.9087 


51.82 


49.09 


43.63 


40.91 


35.45 


130 


10.9545 


52.03 


49.30 


43.82 


41.08 


35.60 


121 


11.0000 


52.25 


49.50 


44.00 


41.25 


35.75 


122 


11.0454 


52.47 


49.70 


44.18 


41.42 


35.90 


123 


11.0905 


52.68 
52.89 


49.91 


44.36 


41.59 


36.04 


124 


11.1355 


60.11 


44.54 


41.73 


36.19 


125 


11.1803 


53.11 


50.31 


44.72 


41.93 


36.34 


126 


11.2250 


53.32 


50.51 


44.90 


42.09 


36.48 


127 


11.2694 


53.53 


60.71 


46.08 


42.26 


36.63 


128 


11.3137 


53.74 


60.91 


45.25 


42.43 


36.77 


129 


11.3578 


53.95 


61.12 


45.43 


42.59 


36.91 


130 


11.4018 


54.16 


61.31 


45.61 


42.76 


37.06 


131 


11.4456 


64.37 


51.50 


45.78 


42.92 


37.20 


132 


11.4891 


54.57 


61.70 


45.96 


43.08 


37.34 


133 


11.5326 


54.78 


51.90 


46.13 


43.25 


37.48 


134 


11.5758 


54.99 


62.09 


46.30 


43.41 


37.62 


135 


11.6190 


55.19 


62.29 


46.48 


43.57 


37.76 


136 


11.6619 


55.39 


62.48 


46.65 


43.73 


37.90 


137 


J 1.7047 
11.7473 


55.60 


52.67 


46.82 


43.89 


38.04 


138 


55.80 


62.86 


47.99 


44.06 


38.18 


139 


11.7898 


66.00 


63.05 


47.16 


44.21 


38.32 


140 


11.8322 


66.20 


63.24 


47.33 


44.37 


38.46 



92 PRACTICAL COTTON CALCULATIONS 

DIAMETERS OF YARNS. 

The question of the diameter of yarns has 
very little bearing on practical calculations. 
About the only practical value that can be 
quoted is that of guiding a person to prevent him 
from attempting to make an impossible construc- 
tion of cloth. 

There is a limit to the sley and pick of a cloth 
that can be woven with a given weave and a 
given amount of material, the number varying 
according to the number of interlacings in the 
weave and the counts of yarn. 

It is well known that yarns of similar counts 
but of different grades of cotton vary in diame- 
ter, the natural tendency of some being to bed 
into each other more than others, thereby form- 
ing a yarn with a smaller diameter. 

A yarn made in a room containing a moisten- 
ing apparatus will also be of smaller diameter 
than one made in a hot, dry room in which there 
is considerable electricity, because the fibres have 
a tendency to cling together better in a damp 
room. 

The diameters of cotton yarns vary inversely 
as the square roots of the counts, and the follow- 
ing is given: 

To Find the Diameter of a Cotton Yarn, or the 
Number of Strands of Cotton Yarn of Any 
Counts that can be Placed Side by Side in 
One Inch. 

Rule 80. Multiply 840 by the counts of yam; 
extract the square root of the answer and deduct 
10% for compression. (See Rule 81.) 



PRACTICAL COTTON CALCULATIONS 93 

Example. What is the diameter of l's yarn? 

840 X 1 = 840; sq. root 840 = 28.98; 10% of 
28.98 = 2.89. 

28.98 — 2.89=26.09 or 26.1, W.t indies, 
diameter of yarn, Ans. 

That is, 26.1 strands of l's yarn can be placed 
side by side in the space of 1 inch. 

As the diameter of No. l's yarn is 1/26.1 
inches, Rule 81 may be substituted for Rule 80. 

Rule 8i. Multiply the square root of the 
counts of yarn by 26.1. 

Example. How many strands of 36 's yarn 
can be placed in 1 inch, flat? 

Sq. root 36 = 6 ; 6 X 26.1 = 156.6, Ans. 

That is, a 36 's yarn is rsi.e inches in diameter. 

The tables on pages 90 and 91 show the squaie 
i«)o1 of all counts from 1 to 140, therefore to find 
the diameter of any cotton yarn it is only neces- 
sary to multiply the square root of the counts 
desired, as found in the table, by 26.1 to give the 
number of strands of yarn of that count that can 
be laid in the space of one inch. 



TESTING YARNS FOR STRENGTH. 

The method generally adopted when testing 
yarns in hank form for strength is to reel one 
lea from each of 1 to 4 bobbins, and place each 
lea separately on a machine made for the pur- 
pose which automatically indicates the breaking 
strength of the yarn. It is advisable to have 



94 PRACTICAL COTTON CALCULATIONS 

the testing machine run by power because when 
making comparative tests the pull on each hank 
should be uniform. 

Yarns of similar counts but different grades of 
cotton vary in breaking strength, and it is impos- 
sible to state just how strong a yarn should be. 
The number of turns or twists per inch will also 
vary the breaking strength. 

By referring to the table on page 96 it will be 
noticed that the yarns do not vary in breaking 
strength in similar proportion to the counts. 



BREAKING WEIGHTS OF AMERI- 
CAN YARNS SPUN FROM 
AMERICAN COTTON. 



• The table on page 96, used by permission of 
Draper Company, Hopedale, Mass., indicates the 
average breaking weights of sample skeins from 
several hundred American mills. 

The old breaking weight referred to in the 
table is an old standard obtained by tests from 
225 mills in 1886, and is here shown for the pur- 
pose of comparison with the new standards. 

The first new table represents average tests of 
carded yarns made from stock averaging about 
strict middling in grade. The combed warp 
table represents tests of yarns made from stock 
slightly under good middling. The table of soft 
twisted yarn is based on yarns averaging 3.25 
times the square root of the counts in twist, the 
stock averaging about strict middling. All the 
yarns were tested on a power tester. 







OLD 


NEW 


NEW 


NEW 






OLD 


NEW 


PJ 


fee 

2 o 


Breaking 

Weight 

of Warp 

Yarn. 


Breaking 

Weight 

of Warp 

Yarn. 


Breaking 
Weight 
Combed 
Warp. 


Breaking 

Weight 

Soft Twist 

Yarn. 




'- <-' 


Breaking 

Weight 

of Warp 

Yarn. 


cj i, e k 


1000 


1 










19.6 


51 


3".6 


47— 


5U0 


2 










19.2 


52 


3.1 


46 


333.3 


3 


530 


634+ 


863— 


620+ 


18.9 


53 


35.5 


45H 




250 


4 


410 


476— 


646 


462 


18.5 


54 


34.9 


44- 




200 


5 


330 


381 


516 


367 


18.2 


55 


34.4 


43- 




166.7 


6 


275 


318— 


429+ 
367+ 


304— 


17.9 


50 


33.8 


42^ 




142.9 


•7 


237.6 


272+ 


258+ 


17.5 


57 


33.4 


42— 


125 


8 


209 


238+ 


321 


224+ 


17.2 


58 


32.8 


41— 


111.1 


9 


186.5 


212+ 


285- 


198+ 


17 


59 


32.3 


4C+ 


100 


10 


168.7 


191 


256 


177 


16.7 


60 


31.7 


39+ 


90.9 


11 


154.1 


174— 


232+ 


160— 


16.4 


61 


31.3 


39— 


83.3 


12 


142 


159+ 
147+ 


213- 


145+ 
133+ 


16.1 


62 


30.8 


38— 


76.9 


13 


131.5 


196 


15.9 


63 


30.4 


37+ 


71.4 


14 


122.8 


137- 


182- 


123— 


15.6 


64 


30 


- 37- 


66.7 


15 


115.1 


128— 


169+ 
158+ 


114— 


15.4 


65 


29.6 


36 


62.5 


16 


108.4 


120— 


106- 


15.2 


66 


29.2 


35+ 


58.8 


17 


102.5 


113— 


149- 


99— 


14.9 


67 


28.8 


35- 


55.6 


18 


97.3 


107— 


140+ 


93- 


14.7 


68 


28.5 


34+ 


52.6 


19 


92.6 


101 


133— 


87 


14.5 


69 


28.2 


34— 


50 


30 


88.3 


96 


126 


82 


14.3 


70 


27.8 


33+ 


47.6 


21 


83.8 


914- 

87+ 


120— 


77+ 


14.1 


71 


27.4 


33- 


45.5 


22 


79.7 


114+ 


73+ 


13.9 


72 


27.1 


32+ 


43.5 


23 


75.9 


84- 


109+ 


70— 


13.7 


73 


26.8 


32- 


41.7 


24 


72.4 


80+ 


104+ 


66+ 


13.5 


74 


26.5 


31+ 


40 


25 


69.2 


77 


100 


63 


13.3 


75 


26.2 


31— 


38.5 


26 


66.3 


ft 


96 


60+ 

57+ 


13.2 


76 


25.8 


30+ 


37 


27 


63.6 


92+ 


13 


77 


25.5 


30— 


35.7 


28 


61.3 


69- 


89- 


55- 


12.8 


78 


25.3 


29+ 


34.5 


29 


59.2 


67— 


86— 


53- 


12.7 


79 


24.9 


29- 


33.3 


30 


57.3 


64H 




83- 


50+ 


12.5 


80 


24.6 


28+ 


32.3 


31 


55.6 


62- 




80— 


46+ 


12.4 


81 


24.3 


28+ 


31.3 


32 


54 


60- 




77+ 


12.2 


82 


24 


28— 


30.3 


33 


52.6 


59— 


75- 


45— 


12.1 


83 


23.7 


27+ 


29.4 


34 


51.2 


57- 


72H 




43— 


11.9 


84 


23.4 


27- 


28.6 


35 


50 


55+ 


70- 




41+ 


11.8 


85 


23.2 


27— 


27.8 


36 


48.7 


54— 


68- 




40- 


11.6 


86 


22.8 


26+ 


27 


37 


47.6 


52+ 


66- 




38+ 


11.5 


87 


22.6 


26- 


26.3 


38 


46.5 


51 


64- 




37 


11.4 


88 


22.4 


26— 


25.6 


39 


45.5 


50— 


63- 


36— 


11.2 


89 


22.2 


25+ 


25 


40 


44.6 


48H 




61 


34- 




11.1 


90 


22 


25- 


24.4 


41 


43.8 


47- 




59+ 


33- 




11 


91 


21.7 


25- 


23.8 


42 


43 


46- 




58- 


32- 




10.9 


92 


21.5 


24+ 


23.3 


43 


42.2 


45- 




56+ 

55+ 


31- 




10.8 


93 


21.3 


24- 


22.7 


44 


41.4 


44- 




30- 




10.6 


94 


21.2 


24— 


22.2 


45 


40.7 


43- 




54— 


29- 




10.5 


95 


21 


23+ 

23+ 


21.7 


46 


40 


42- 




53— 


28- 




10.4 


96 


20.7 


21.3 


47 


39.3 


41- 




5H 




27- 




10.3 


97 


20.5 


23- 1 


20.8 


48 


38.6 


41- 


50- 




27— 


10.2 


98 


20.4 


23— I 


20.4 


49 


37.9 


40— 


49- 




26- 


10.1 


99 


20.2 


22+ 


30 |50 


37.3 


39 


48 


25 


10 


100 


20 


22 



PRACTICAL COTTON CALCULATIONS 



07 



Yards of Cloth per loom per day of ten hour* 



Picks 

per 
inch 



Picks per minute. 



83.3 
75.8 
1.9.4 
(54.1 

59.5 

5 r..<; 

52.1 
4tt.O 
46.3 
43.'.l 
41.7 

39. 7 

37.9 

3 c. 2 

34.7 
33.3 
32.1 

3H.0 

29. X 
28.7 
27 



1 I >2 
104 
L06 

IDS 

no 

12 
1 14 

L6 
1 18 

i ao 

124 
1 26 
I2S 
130 
134 
136 
140 
144 
146 



156 
160 

164 
166 
170 

174 

176 1 
180 



26.9 

21',. 1 1 

2:..:'. 

24.5 

23.x 

23.1 

22.5 

21.9 

21.4 

2H..S 

20.3 

10.3 

19.4 

18.9 

18.5 

18.1 

17.7 

17.4 

17.0 

16.7 

16.3 

16.0 

15.7 

15.4 

15.2 

14.9 

14.6 

14.4 

14.1 

13.9 

13.7 

13.4 

13.2 

13.(1 

12.X 

12.4 

12.3 

11.9 

11.6 

11.4 
11.1 

1(1. X 
K).7 
1(1.4 
ld.2 
l(i.(i 



100 105 110 115 | 130 



87.5 
79.5 
72.9 
67.3 
62.5 
5S.3 
54.7 
51.5 
48.6 
46.1 
43.7 
41.7 
39.8 

3.X.O 

36.5 

.-.5.(1 
33.7 
32.4 
31.3 
3<>.2 
2'l.2 
28.2 
27.3 
2 6.5 
25.7 
25.(1 
24.3 
23.6 
23..) 
22. 1 
21.9 
21.3 
2.0.X 
20.3 
19.9 
19.4 
19.0 
18.6 
18.2 
17.9 
17.5 
17.2 

16.8 

16.5 

16.2 

15.9 

15.6 

15.4 

15.1 
14.X 
14.6 
14.3 
14.1 
13.9 
13.7 
13.5 
13.1 
12.9 
12.5 
12.2 
12.(1 
11.7 
11.4 
11.2 
10.9 
10.7 
10.6 
lo.3 
10.1 

9.9 

9.7 



61.1 

57.3 
53.9 
50.9 

4 8.2 
45.8 
43,. 7 

11.7 
39.9 

38.2 

36.7 

35.3 
34.0 
32.7 
31.6 

30.6 
29.6 

28.6 
27.8 
27.0 
26.2 
25.5 
24.X 
24.1 
23.5 
22.9 
22.4 
21.8 
21.3 
2(1.8 
20.4 
19.9 
19.5 
19.1 
18.7 
18.3 
18.0 
17.6 
17.3 
17.0 

16.7 

16.4 

16.1 

15.8 

15.5 

15.3 

15.0 

14.8 

14.6 

14.3 

14.1 

13.7 

13.5 

13.1 

12.7 

12.6 

12.2 

11.9 

11.8 

11.5 

11.2 

11.0 

10.8 

10.5 

K).4 

10.2 



79.9 
73.7 

68.5 
63.9 
59.9 
56.4 
53.2 
50.4 
47.9 
45.6 
43.6 
11.7 
39.9 
38.3, 
36.9 
35.5 
3 4.2 
33.(1 
31.'.) 
.-.('.9 
29.9 
29.0 
28.2 
27.4 
26..; 

25.9 

25.2 

24.6 

24.0 

23.4 

22.; 

22.3 

21.X 

21.3 

20.x 

20.4 

211.0 

19.6 

19.2 

18.8 

18.4 

18.1 

17.7 

17.4 

17.1 

16.8 

16.5 

16.2 

16.0 

15.7 

15.5 

15.2 

15.0 

14.7 

14.3 

14.1 

13.7 

13.3 

13.1 

12.8 

12.4 

12.3 

12.0 

11.7 

11.5 

11.3 

11.0 

10.9 

10.6 



loo.o 
90.9 
83.3 
76.9 
71.4 
66.7 
62.5 
58.8 
55.6 
52.6 
5(). O 
47.6 
45.5 
43.: 
41.7 
40.0 
38.5 
37 
35.7 
34.5 
333 
32 

31 

30.3 

29 4 

28 6 

2 7 X 

27 O 

26 3 

25 6 

25.0 

24.4 

23.8 

23.3 

22.7 

2 

21.7 

21.3 

2o.8 

20.4 

20 

19.6 

192 

18.9 

18.5 

18.2 

17.9 

17.5 

17.2 

16.9 

16.7 

16.4 

16.1 

15.9 

1 5.6 

15.4 

14 .9 

14 7 

14 

13 9 

13 7 

13.3 

13.1) 

12 8 

12.5 

12.2 

12() 

11 X 

11.5 

11.4 

111 



104.2 
94 7 
86 
80 
74.4 
69.4 
65.1 
61.3 
57.9 
54 
52 
49.6 
47.3 
45.3 
43.4 
41 7 
40.1 
38.6 
37 2 
35.9 
34.7 
33.6 
32 6 
31.6 
3(). 6 
29.8 
28 
28.2 
27.4 
26. 
26.0 
25.4 
24.X 
24 2 
23 7 
23 
22 6 
22 2 
21 7 
21 3 
2(1.8 
2(14 
2().() 
19 7 



16.0 

15.5 

16 

14 

14.5 

14. 

13.9 

13.5 

13.4 

13(i 

12.7 

12.6 

12 

12.0 

11.8 

11 6 



1(18.3 
98.5 
90.3 
83.3 
77.4 
72.2 
67.7 
63.7 
60. 2 
57.0 
54.2 
51.6 
49,2 
47. 
45. 
43.3 
41.7 
40. 



34.9 

33.9 
32.8 
31.9 
31.0 
30.1 
29.3 
28.5 
27.8 
27.1 
26.4 
25.8 
25.2 
24.6 
24.1 
23.6 
2 3.o 
22.6 
22.1 
21.7 
21.2 
2o.x 
2(1.4 
20.1 
19.7 
19.3 
19.(1 
18.7 
18.4 
18.1 
17.8 
7.5 



13.5 



112.5 
102.3 
93.7 
86.5 
80.4 
75.0 
70.3 
66.2 
62. 
59.2 
56.3 
53.6 
51.1 
48.9 
46.9 
45.0 
43.3 
41,7 
40.2 
38.8 
37.5 
36 
35.2 
34, 
33 
32, 
31.3 
30.4 

29.6 

28.8 

28.1 

27.4 

26.8 

26.2 

25.6 

25.li 

24 

23.. 9 

23.4 

23. 

22.5 

22, 

2 1 6 

21.2 

2(1.8 

20.5 

L'O.l 

19.7 

19.4 

19.1 



17.2) 17.9 



6.9 
16.7 

16.2 
15.9 
15.5 
15.0 
14.8 
14.4 
14 1 
13.9 
13.5 
13.2 
13.1 
12.7 
12.5 
12.3 
12..) 



17..; 

17.3 
16.8 
16.5 
16, 

15.6 
15.4 
15..) 
14.6 
14.4 
14.1 
13.7 
13.5 
13.2 
12.9 

12.8 __ 
12.5| 13.0 



116.7 

106.1 

97. 

89.7 

83.3 

77. 

72.9 

f.X.C, 

64.8 

61.4 

58.3 

55.6 

53.0 

50.7 

48.6 

46.7 

44.9 

43.2 

41.7 

403 

38.: 

37.6 

3.6.5 

35.4 

34.3 

33.3 

32.4 

3.1.5 

293) 

29.2 

28.5 

27.X 

27.1 

2< ',.5 

25.9 

25.4 

24.8 

24.3 

23.8 

23.3 

22. 

22.4 

22.(1 

21.6 

21.2 

20.8 

20.5 

20.1 

19.8 

19.4 

19.1 

18.8 

18.5 

18.2 
17.9f 
17.4 
17 

16.7 
16.2 
16. (I 
15.6 
15.2 
15.(1 
14.6 
14.2 
14.1 
13.7 
13.4 

13.; 



xo.c, 
75.5 
7 
67.1 

6,3.6 

6(1.4 

57.5 

54 

52.5 

5(13 

48 3 

46.5 

4 18 

43 2 

41.7 

403 

39.0 

37.8 

36.6 

35 5 

34 

33 6 

32.7 

31 8 

.-,1 
30.2 

29.5 

28.8 

27.5 
26.9 
26.3 
25 7 
25 2 



125.(. 
113.6 
K>4.2 
96.2 
89.3 
83.3 
78. 
73.5 
69.4 

62.5 

59, 

56.8 

54,3 

52.1 

50.0 

48.1 

46.3 

44.6 

43.1 

41.7 

40.3 

39.1 

37.9 

3,6.8 

35.7 

34.7 

33.8 

32.9 

32.1 

31.3 

30.5 

29.' 

2X.4 

2-7. X 

27.2 

26, 

26,.0 



23.2J 24.0 



22.X 

22.4 

22.o 

21.6 

21.2 

20.: 

20.5 

20.1 

19.8 

19.5 

19.2 

18.9 

18, 

18.1, 

17.8 

17.3 

16.8 

16.6 

16.1 

15.7 

15.5 

15.1 

14.7 

14.6 

14.2 

13.9 



13. 



23 

25.1 

22.7 

22.3 

21.9 

21.6 

21.2 

2(1.8 

2(1.4 

2. ). 1 

19.8 

19.5 
19.2 
18.7 
18.4 
17.9 
17.4 
17.1 
16.7 
16.2 
16.0 
15.6 
15.2 
15.1 
14.7 
14.4 
14.2 
13.9 



PRACTICAL COTTON CALCULATIONS 



Yards of Cloth per loom per day of ten hours. 



Picks 














per 






Picks per minute. 




inch 














20 


155 


160 165 

133.3 137\5 


170 


175 


180 

150.( 


1 185 1 190 
154.2 158.3 


195 

162.E 


200 


205 


1 20.2 


141.7 


145.8 


100.7 


170.8 


22 


117.4 


121.2 125.0 


128.8 


132.0 


130.4 


140.21143.! 


147.7 


151.5 


155.3 


24 


1(>7.( 


111.1 


114.0 


118.1 


121.5 


125.( 


128.6 


131.0 


13.5.4 


138.0 


1 12.4 


20 


00.4 


]02.< 


105.8 


100.( 


1 1 2.2 


115.4 


'118. ( 


121.8 


125.1 


128.2 


13.1.4 


28 


112.3 


05.2 


08.2 


101.2 


104.2 


1(17.1 


110.] 


113.1 


110.1 


1 19.0 




30 


80.1 


88 '. 


01.7 


04.4 


97.2 


10().( 


102.S 


105.5 


108.: 


111.1 


lT33l 


32 


80.7 


83.3 


85.0 


88.5 


01.1 


03.'. 


00, 


00 () 


lol.l 


UI4.2 


IOC. 8 


34 


70.0 


78. 4 


80.9 


83.3 


85.8 


88.2 


0O.7 


03.1 


05. ( 


08. () 


100.5 


3(3 


71.8 


74.1 


70.4 


78.7 


81.0 


8:;.: 


85. ( 


88.0 


oo.: 


02 


04.0 


38 


68.1 


70.2 


72.4 


74.0 


70.8 


78.; 


81.1 


83.3 


85.C 


87.7 


80.0 


40 


04.0 


00.7 


08.7 


70.8 


72.0 


75.( 


77.1 


70.2 


8i.: 


83.3 


85.4 


42 


01.5 


03.5 


05.5 


07.5 


00.4 


71.4 


73.4 


75.4 


77.4 


70.4 


81.3 


44 


58.7 


00.0 


02.5 


04.4 


00.3 


08.2 


70.1 


72.0 


73.: 


75,x 


77.7 


41! 


50.2 


58.1 


50.8 


01.0 


03.4 


65.2 


07.( 


08.8 


7o.7 


72.5 


74.3 


48 


53.8 


55.0 


57.3 


59.0 


0(1.8 


02. f 


04.'. 


GG.O 


07.7 


69.4 


71.2 


50 


51. 7 


53.3 


55.0 


56.7 


58.3 


C,ll.( 


61.7 


03.3 


05.( 


00.7 


08.3 


52 


49.7 


51.3 


52.0 


54.6 


50.1 


57.7 


50.3 


OO.O 


62.5 


04.1 


05.7 


54 


47. 8 


40.4 


50.0 


52.5 


54.0 


55.0 


57.1 


58.0 


60.2 


01.7 


63.3 


66 


40.1 


47.6 


40.1 


5(1.0 


52.1 


53. ( 


55.1 


50.5 


r>8.( 


59 5 


61.0 


58 


44.5 


40.0 


47.4 


4S.8 


50.3 


51.7 


53. l 


54.0 


5C,.( 


57.5 


58. :i 


60 


43.1 


14.4 


45.K 


47.2 


48.0 


5( u 


51.4 


52.8 


54.2 




56.9 


02 


41.7 


13.0 


44.4 


45.7 


47.0 


48.4 


40.7 


51.1 


52.4 


5 3'; 8 


55 1 


64 


40.4 


41.7 


43.0 


44.3 


45.0 


40.1 


48.2 


40.5 


5(1.8 


52.1 


53.4 


66 


30.1 


4(1.4 


41.7 


42.0 


44.2 


45.5 


40.7 


48.0 


49.2 


5(1.5 


51.8 


CM 


38.0 


39.2 


40.4 


41.7 


42.0 


44.1 


45.3 


40.0 


47.8 


40.O 


5(1.2 


-o 


36.9 


38.1 


30.3 


40.5 


41.7 


4 2.; 


44.( 


45.2 


40.4 


47.0 


48.8 


72 


35.9 


37.0 


38.2 


39.4 


1(1.5 


41.7 


42.8 


44. 


45.1 


40.3 


47.5 


74 


34. o 


36.0 


37.2 


:;.x.:: 


30.4 


4(i.5 


41.7 


42.8 


43.: 


45.() 


40.2 


70 


34. (> 


:;.->. i 


30.2 


37.3 


38.4 


30.5 


40.( 


41.7 


42.8 


43.0 


45.0 


78 


33.1 


34.2 


35.3 


30.3 


37.4 


::x.r. 


3o.r 


40.6 


41.7 


42.7 


43.8 


80 


32.3 


33.:'. 


::i.t 


35.4 


30.5 


37.5 


38.: 


39.6 


40.1 


41.7 


4 2.7 


82 


3 1 .:■ 


32.5 


3.-',. 5 


34.6 


35.0 


30.0 


37.( 


38.6 


30.1 


40.7 


41.7 


84 


30.8 


.-.1.7 


32.7 


:;::.7 


34.7 


35.7 


30,.( 


37.7 


3X.7 


30.7 


4o.7 


86 


30.0 


31.0 


32.0 


32.0 


33.9 


34.9 


35.8 


30.8 


37., x 


38.8 


30.7 


88 


29.4 


.".u..-', 


31.3 


32.2 


33.1 


34.1 


35.1 


30. o 


36.1 




38.x 


90 


2S. 7 


20.0 


30.6 


31.5 


32.4 


33.3 


34.3 


35.2 


30.1 


37.(1 


38.0 


92 


28.1 


20.(1 


20.0 


30.8 


31.7 


3.2. 


33.5 


34.4 


35.3 


30.2 


37.1 


04 


27.5 


28.4 


20.3 


30.1 


31.0 


31.0 


32.x 


33.7 


34.0 


35.5 


30.3 


96 


20.9 


27. S 


28.6 


20.5 


30.4 


31.3 


32.1 


33.0 


33.; 


34.7 


35.0 


98 


26.4 


27.2 


28.1 


28.0 


20.8 


30.0 


31.6 


32.3 


33.2 


34.0 


34.0 


100 


25.8 


20.7 


27.5 


28.3 


20.2 


30.0 


30.8 


31.7 


32.5 


33.3, 


34.4 


102 


25.3 


20.1 


27.0 


27.8 


28.0 


29.4 


30.2 


3 1 .0 


81.9 


32.7 


33.5 


104 


24.8 


25.0 


20.4 


27.2 


28.0 


28.8 


20.0 


30.4 


3 1 .3 


32.1 


32.0 


106 


24.4 


25.2 


25.0 


20.7 


27.5 


28 3 


20.1 


20.0 


30.7 


31.4 


32.2 


108 


23.0 


2 1.7 


25.5 


20.2 


27.(1 


27.S 


28.5 


20.3 


30.1 


30.0 


31.6 


110 


23.5 


24.2 


25.(1 


25.S 


20.5 


27.3 


2X.( 


28.8 


20.5 


30.3 


31.1 


1 12 


23.1 


23. S 


24.0 


25.3 


20.(1 


20.8 


27.5 


28.3 


20.O 


20.8 


30.5 


114 


22.7 


23.4 


24.1 


24.0 


25.0 


20.3 


27. 


27.8 


28.5 


20.2 


3O.0 


116 


22.:; 


23.0 


23.7 


24.4 


25.1 


25.0 


26.6 


27.3 


28.0 


28.7 


20.5 


118 


21.0 


22.0 


2:',..". 


24.(1 


24.7 


25.4 


26.1 


20.8 


27.5 


28.2 


29.0 


ISO 


21.5 


22.2 


22.0 


23.6 


24.3 


25.0 


25.7 


26.4 


27.1 


27.8 


28.5 


L22 


21.2 


21.0 


22.5 


23.2 


23.0 


24.0 


25.3 


20.0 


20.0 


27.3 


28.0 


124 


20.8 


21.5 


22.2 


22.8 


23.5 


24.2 


24.9 


25.5 


20.2 


20.0 


27.0 


126 


20.5 


21.2 


21.8 


22.5 


23.1 


23.8 


24.5 


25.1 


25,x 


20.5 


27.1 


128 


20.2 


20.8 


21.5 


22.1 


22.8 


23.4 


24.1 


24.7 


25.4 


20.0 


20.7 


130 


10.0 


2(1.5 


21.2 


21.8 


22.4 


23.1 


23.7 


24.4 


25.o 


25.0 


20.3 


134 


10.3 


10.0 


20.5 


21.1 


21.8 


22.4 


23.0 


23.0 


24.3 


24.0 


25.5 


130 


10.0 


10.0 


2().2 


2d.8 


21.4 


22.1 


22.7 


23.3 


23.0 


24.5 


25.1 


140 


18.5 


10.0 


10.0 


20.2 


20.8 


21.4 


22. o 


22.0 


23.2 


23.8 


24.4 


144 


17.0 


18.5 


10.1 


10.7 


2(1.3 


2H.8 


21.4 


22.0 


22.0 


23.1 


23.7 


140 


17.7 


18.3 


18.8 


10.4 


20.0 


2(1.5 


21.1 


21.7 


22.3 


22.8 


23.4 


150 


17.2 


17.8 


18.3 


18.0 


10.4 


20.0 


20.0 


21.1 


21.7 


22.2 


22.8 


154 


10.8 


17.3 


17.0 


18.4 


18.0 


1 0.5 


20.0 


20.0 


21.1 


21.0 


22.2 


150 


10.0 


17.1 


17.0 


18.2 


18.7 


10.2 


10.x 


20.3 


20.8 


21.4 


21.0 


160 


10.1 


10.7 


17.2 


17.7 


18.2 


18.7 


19.3 


10.8 


20.3 


20.8 


21.4 


104 


15.8 


10.3 


10.8 


17.3 


17.8 


18.3 


18.8 


10.3 


10.8 


20.3 


20.8 


ICO 


15.0 


'16.1 


10.0 


17.1 


17.0 


18.1 


18.0 


10.1 


1 0.0 


20.1 


20.0 


170 


15.2 


15.7 


10.2 


10.7 


17.2 


17.0 


18.1 


18.0 


10.1 


10.0 


20.1 


174 


14.8 


15.4 


1 5.8 


10.3 


10.8 


17.2 


17.7 


18.2 


18.7 


10.2 


10.6 


170 


14.7 


15.2 


15.0 


10.1 


10.0 


17.0 


17.5 


18.0 


18.5 


18.0 


10.4 


180 


14.4 


14.8 


15.3 


15.7 


16.2 


16.7 


17.1 


17.6 


18.1 


18.5 19.0| 



CLOTH PRODUCTION. 



To Find Production of Cloth per Week of 56, 
58, 60, or 66 Hours, at Any Desired % 
from 50 to 100, Running in 5's. 

Rule 82. Multiply the speed of the loom by 
the constant desired in the following list and 
divide by the number of picks per inch. 





Constant 


Constant 


Constant 


Constant 


Per Cent, of 


to us<> i'< >r 


to use for 


to use for 


to use for 


production. 


56 hours. 


58 hours. 


60 hours. 


66 hours. 


50 


46§ 


48* 


50 


55 


55 


51* 


53* 


55 


60.5 


60 


56 


58 


60 


66 


65 


601 


621 


65 


71.5 


70 


65* 


67f 


70 


77 


75 


70 


72* 


75 


82.5 


80 


74f 


77* 


80 


88 


85 


79* 


82* 


85 


93.5 


90 


84 


87 


90 


99 


95 


88f 


91* 


95 


104.5 


100 


93* 


96f 


100 


110 



Example. What is the production in yards 
per week of 60 hours of a loom running 160 
picks per minute, weaving- a cloth with 120 
picks per inch, at 80% ? 

160 picks X 80 constant „_„ 

z~ — r~r— — : — ; = 106^ vards, Ans. 

120 picks per inch * 

The preceding constants are based on the 
following: L0FC> 



100 PRACTICAL COTTON CALCULATIONS 

60 minutes X hours per week X % production 
36 inches per yard 

The cloth production tables on pages 97 and 
98 are based on 100% production for 10 hours, 
no allowance being made for stoppages. 

Owing to the tables being computed for 10 
hours, they are very convenient when requiring 

To Find % Production of a Loom when Hours 
Run, Speed of Loom, Picks per Inch and 
Actual Production in Yards are Known. 

Rule 83. Multiply picks per inch by yards 
produced and by .6, and divide by speed of loom 
and number of hours run 

The .6 is obtained by dividing 36 inches per 
yard by 60 minutes per hour. 

Example. The actual production of a loom 
running 150 picks per minute, weaving a cloth 
with 80 picks per inch, is 23 yards, in 10 hours. 
What is the % of production? 

80 picks per inch X 23 yards X -6 „ . 

150 speed of loom X 10 " i6 ' b/ °' Am ' 

To Find Production of Cloth, in Yards per Loom, 
for Any Number of Hours, at Any Desired %. 

Rule 84. Multiply the production for 10 
hours at 100% (see tables, pages 97 and 98) by the 
number of hours run and the % of production 
desired, and divide by 10. 

Example. A cloth with 60 picks per inch is 
desired to be woven on a loom running 160 picks 
per minute. What would be the production 
per week of 58 hours at 80% ? 



PRACTICAL COTTON CALCULATIONS ]01 

According to the table the production for 10 
hours at 100% would be 44.4 yards, therefore 

44.4 vards X 58 hours X .80 ^ n . 

^r^j — — — 20C) vds., Ans. 

10 hours 

Rule 82 may be used 
To Find the Number of Cuts per Loom per Week 
by dividing the number of yards per week by 
the length of the cut. 



LOOM CALCULATIONS. 

To Find Constant to Use for Any Loom Take-Up 
Motion. 
Rule 85. Multiply all the driven gears to- 
gether and divide by all the drivers multiplied 
togt I her. 

The circumference of the sand roller in inches 
is considered a driver. If the motion takes up 
every two picks, the driven gears should be mul- 
tiplied by 2. 

It is customary to allow a certain % for the 
difference between the picks per inch in the 
cloth while in the loom and after leaving the 
loom. This may be done by deducting a cer- 
tain % , varying from 1 to 2%, according to the 
motion used, from the circumference of the 
sand roller. 

To Find Change Gear or Picks per Inch on Looms 
where the Change Gear is a Driver, when 
Constant is Known. 
Rule 86. Divide the constant by picks per 



102 PRACTICAL COTTON CALCULATIONS 

inch to find change gear. Divide constant by 
change gear to find picks per inch. 

When the change gear is a driver, the con- 
stant is always a dividend. 

To Find Change Gear or Picks per Inch on Looms 
where the Change Gear is a Driven Gear, 
when Constant is Known. 

Rule 87. Divide picks per inch, by constant 
to find change gear. Multiply change gear by 
constant to find picks per inch. 

The sand roller gear and every alternate gear 
from that are driven gears. All the remaining 
gears are drivers. 



SPEED CALCULATIONS. 

To Find Speed of Shafting, when Diameter of 
Driving Pulley, Diameter of Loom Pulley, 
and Speed of Loom are Known. 

P.ule 88. Multiply diameter of loom pulley 
by speed of loom, and divide by diameter of 
(hiring pulley. 

Example. What is the speed of shafting 
required to run a loom 145 picks per minute, 
with a 14-inch pulley on the loom and a 7-inch 
pulley on the shaft? 

14-inch pulley on loom X 145 picks per minute 
7-inch pulley on shaft 
= 290 revolutions per minute, Ans. 



PRACTICAL COTTON CALCULATIONS 103 

To Find Diameter of Driving Pulley, when Speed 
of Shafting, Diameter of Loom Pulley, and 
Speed of Loom are Known. 

Rule 89. Multiply diameter of loom pulley 
by speed of loom, and divide by speed of shaft- 
ing. 

Example. What diameter of pulley will be 
required on a shaft running; 290 revolutions per 
minute to run a loom 145 picks per minute with 
a 14-inch pulley? 



14-inch pulley X 145 picks per min. . 

diameter oi 
driving pulley, Ans 



290 R. P.M. diameter of 



To Find Diameter of Loom Pulley, when Speed 
of Loom, Speed of Shafting, and Diameter of 
Driving Pulley are Known. 

Rule 90. Multiply speed of shafting by 
diameter of driving pulley, and divide by speed 
of loom. 

Example. A loom is required to run 145 
picks per minute. The speed of the shaft is 290 
R. P. M. and the diameter of the pulley on the 
shaft is 7 inches. What diameter of loom pul- 
ley will be required? 

290 R. P. M. X 7 ins. driving pulley , t . 

— — — : — 5_j: ^- = 14 ms. 

145 picks per mm. diameter of 

loom pulley, Ans. 



104 PRACTICAL COTTON CALCULATIONS 

To Find Speed of Loom, when Speed of Shafting, 
Diameter of Driving Pulley, and Diameter of 
Loom Pulley are Known. 

Rule 91. Multiply speed of shafting by diam- 
eter of driving pulley, and divide by diameter of 
loom pulley. 

Example. What will be the speed of a loom 
with a 14-inch pulley, the speed of shafting 
being 290 R. P. M. and the diameter of the driv- 
ing pulley 7 inches? 

290 R. P. M. X 7 ins. driving pulley ,,_ . . 

... . =— „ — -= 145 picks 

14-m. loom pulley per min ? Am 

The four preceding rules, 88 to 91, may be 
summarized in the following — 

Formula D. To Find Speed of Shafting, Diameter 
of Driving Pulley, Diameter of Loom Pulley, 
or Speed of Loom. 

Speed of shafting X diameter of driving pulley 

is equal to 

Diameter of loom pulley X speed of loom. 

Rule. Divide the product of the remaining 
items of the group containing the required item 
into the product of the other group. 

When the numbers found are too large for 
practical purposes, use smaller numbers that are 
in direct ratio with them. 



COST CALCULATIONS. 



To Find Weaving* Cost per Yard when Weekly 
Rate and Production are Known. 

Rule 92. Divide the weekly rate by the pro- 
duction in yards per week. 

Example. If the production of a loom is 150 
yards per week, the weekly rate $9.75, and the 
looms per set 5, what would be the weaving price 
per yard of cloth? 

150 yards X 5 looms = 750 yds. per week 

$9.75 weekly rate ., rt . , 

=— — - — 1.3c. weaving cost per yd., 

750 yds. per week to F J A ' MS 

$9.75 M ._ 

or^-r; — — == $1.95 per loom 
5 looms 

$1.95 , _ . , , 

— 1.3c. weaving cost per yd., 



150 yards per loom j Lng 

To Find Weaving Cost per Cut when Weekly 
Rate, Length of Cut, and Production per 
Week are Known. 

Rule 93. Multiply the weekly rate by the 
length of cut and divide by the production per 
week. 

Using the preceding example what would be 
the weaving cost per cut of 100 yards? 



106 PRACTICAL COTTON CALCULATIONS 

$9.75 weekly rate X 100 yds, cut length 

750 yds. production per week weaving 

cost per cut, Ans. 

To Find Cost per Yard for Oversight when Pro- 
duction and Oversight per Loom per Week 
are Known. 

Rule 94. Divide the oversight per loom by 
the production. 

Example. If a plain loom produces 160 
yards per week, and the oversight per loom per 
week is 31 cents, what would be the oversight 
cost per yard? 

31c. oversight -, no ^r • w i 

— -^ — = .19375c. oversight per yard, 

160 yards Am 

To Find General Expense per Yard when Produc- 
tion and General Expense per Loom per Week 
are Known. 

Rule 95. Divide the general expense per loom 
by the production. 

Example. If a loom produces 145 yards per 
week, and the general expense per loom is $1.74, 
what would be the cost per yard for general 
expense ? 

$1.74 

— r^ 7- = 1.2c. general expense per yd., Ans. 

145 yards 

To Find General Expense per Pound of Cloth 

when General Expense per Loom, Yards per 

Week per Loom and Number of Yards per 

Pound are Known. 

Rule 96. Multiply the general expense per 



PRACTICAL COTTON CALCULATIONS 107 

loom by the number of yards per pound and 
divide by the number of yards per week. 

Example. If the general expense in a mill 
is estimated at $1.80 per loom per week, what 
would be the general expense per pound of a 
piece of cloth 5.3 yards per pound produced at 
the rate of 130 yards per week per loom ¥ 

$1.80 genl. expense per loom X 5.3 yards per lb. 
130 yards per week 
= 7.338c. genl. expense per lb, Ans. 

To Find Cost of Stock per Pound of Cloth, in a 
Cloth Containing More than One Quality of 
Cotton and More than One Counts of Yarn 
when Cost of Cotton per Pound and % of 
Each Counts of Yarn are Known. 

Rule 97. Multiply the % of each yarn by the 
cost of cotton per pound. Add results. 

Example. A cloth contains 37% of 9c. cot- 
ton and 63% of 12c. cotton. What is the cost 
of stock per lb of cloth ? 

37% or .37 X 9c. = 3.33 
63% or .63 X 12c. = 7.56 



10.89c. per It), Ans. 

To Find Cost of Yarns per Cut when Weight and 
Cost per Pound of Each are Known. 

Rule 98. Multiply the weight of each by the 

cost per pound. Add results. 

Example. A cloth contains 5 lbs. of warp 
and 4J lbs. of filling. If the warp costs 18c. 



108 PRACTICAL COTTON CALCULATIONS 

and the filling 19c. per lb., what would be the 
cost of the yarns in the cloth ? 

5 lbs. warp X 18c. = .90 
4.5 lbs. warp X 19c. = .855 



$1,755, Ans. 

To Find Cost of Yarns per Yard of Cloth when 
Total Cost of Cut and Length of Cut are 
Known. 

Rule 99. Divide the cost per cut by the length. 

Example. The yarn in a cut of cloth 100 
yards long cost $3.80. What is the cost of the 
yarns per yard of cloth? 

= 3.8c. cost of yarns per yard, Ans. 



100 vards 



To Find Cost of Yarns in a Warp when Counts, 
Length, Number of Ends and Price per Pound 
are Known. 

-KRule ioo. Multiply the length of fit? warp in 
yards by the number of ends in the warp and the 

price per pound and divide by 840 and the yarn 

counts. 

Iv\ ample. A cotton warp 1200 yards long 
contains 2700 ends of 35 's yarn. The yarn price 
is 26c. per pound. What is the cost of the 
warp ? 

2700 ends X 1200 yards X 26c. _ 

840 X 35 's warp counts " * - ' * 



PRACTICAL COTTON CALCULATIONS 109 

To Find Cost of Filling in a Piece of Cloth when 
Length of Piece, Width in Reed, Pick, Counts 
and Price per Pound of Filling are Known. 

*Rule 101. Multiply length of pieee by width 

in reed, picks per inch and price per pound, and 
divide by 840 and the filling counts. 

Example. A cut of cloth 56 yards long is 
woven 30 inches wide in the reed with 70 picks 
per inch of 40 's filling'. The cost of the filling 
is 25 cents per pound. What is the cost of the 
filling per cut? 

56 yards X 30 inches in reed X 70 pick X 25c. 
840 X 40 's filling counts 

= 87.5c. cost of filling, Ans. 



COSTS OF CLOTH. 

In cloth mills the product from which the 
income is realized is cloth, therefore the most 
important branch of textile calculations in a 
cloth mill deals with cost. 

The cost of a piece of cloth, which is figured 
at so much per yard, or so much per pound, or 
both, is usually estimated in the office from 
items furnished by the various overseers. 

As all textile calculations enter either directly 
or indirectly into, and lead up to the final cost 
of the cloth, the rules in the earlier part of this 
book are given, although all of them are not 
necessary for any one piece of cloth. 



110 PRACTICAL COTTON CALCULATIONS 

The preceding rules have been given so that 
any one item may be found with very little 
trouble, and it is intended in the succeeding 
pages to show how the cost of any cloth may be 
ascertained. 

As the methods of estimating costs vary in 
different mills, one method only will be ex- 
plained here; part of the items dealt with in 
explaining this, or other items calculated from 
them, are usually required in every mill. 

For convenience in dealing with mill calcu- 
lations it is customary to use what are termed 
blanks, upon which are printed various items. 
Against these items overseers of the various 
departments write out the necessary data. In 
the system to be explained here it will first be 
shown how the various items necessary to fill out 
the weave-room blank are obtained, then how the 
total cost per yard and per pound of cloth are 
estimated. 

In the following blank the words shown in 
italic type are supposed to be printed. The 
remaining figures and letters show the data nec- 
essary for the production of a certain piece of 
cloth, which will be taken as an example in ex- 
plaining the items and how they are obtained. 



PRACTICAL COTTON CALCULATIONS 111 

System of Filling Out Blank with Weave Room 
Data for a Piece of Cloth. 

BLANK NUMBER 1. 

1. Pattern number. 26. 

2. Kind of cloth. Leno. 

3. Sley. 56 L pick 8(X 

5. Warp counts, No. of ends of each, and con- 

traction and size. 
200 ends 4/32 's, 20% contraction. 
300 ends 2/32's, 15% contraction. 
2184 ends 50 's, 10% contraction and size. 

6. Filling counts. 60 's. 

7. Width of cloth. 28 inches. 

8. Width in reed. 30 inches. 

9. Yards per pound. 6.02. 

10. Looms per set, 4. 11. Speed, 150. 

12. Per cent, of production. 80. 

13. Weekly rate. $10.00. 

14. Yards per week {58 hours). 145. 

15. Weaving cost per yard. 1.724c. 

16. Counts and weight of yarn in 100 yards of 

cloth. 
Warp. 4/32 's, 3.56 pounds. 
2/32's, 2.56 
" 50 's 5 72 " 

17. Filling. 60 's, 4.76 



18. 16.60 pounds, Total weight in 

100 yards of cloth. 



112 PRACTICAL COTTON CALCULATIONS 

Explanation of Items in Weave Room Blank. 

1. Pattern number. This item will readily 
explain itself. 

2. Kind of cloth. Against this is placed 
leno, plain, bedford cord, etc., according to style 
made. 

3 and 4. Sley and Pick. These are found 
from the cloth to be made by the designer, or by 
the weave room overseer, if the latter does the 
designing. The count of the cloth mentioned 
here is 56 X 80. The 128 shown under the sley 
reed represents the average sley, and is found 
from items 5 and 7 by Rule 51 as follows: 
3584 total ends 
28 ins. width of cloth = 128 average sley ' 

The average count of the cloth is 128 X 80. 

5. Warp counts, No. of ends of each, and con- 
traction and size. The warp counts are usually 
found by comparison, as explained on page 12, 
or by weighing as in Rule 1. The number of 
ends of each counts are obtained by Rule 25. 
The amount to allow for contraction and size are 
estimated by the designer. 

Ply cotton yarns are not usually sized. 

6. Filling counts. If the weight of the cloth 
is of secondary importance, which is usually the 
case in fancy cotton goods, the filling is varied, 
if necessary, until a counts is obtained that 
makes the appearance of the cloth satisfactory. 
When the counts of the filling is decided upon 
in this manner, the yards per pound, item 9, 
may be found by Rule 68, after finding 
item 18. See example after explanation of item 



PRACTICAL COTTON CALCULATIONS 113 

9. If items 5 and 9 are found before the filling 
counts, the latter may be found from items 4, 8 
and 17 by Rule 37. 

Example. 
80 pick X 30 in. at reed X 100 yds. _ 

840X4.76 lbs. of filling -^ 

filling. 
Note how the weight of the filling, item 17, is 
obtained. 

7. Width of cloth. This is usually given to 
the designer by the superintendent. 

8. Width at reed. This may be found from 
items 3 and 7 by Rule 63. 

Example. 

56 sley X 28 inches width of cloth 
26.19 dents per inch in reed X 2 ends per dent 
= 29.93 inches, say 30 inches width in reed 

In the table on page 68 a 56 sley gives 26.19 
dents per inch in the reed. 

In dealing with the contraction of a fancy 
cloth it is necessary that a person should have 
considerable practical experience before he can 
judge what to allow for contraction, and it is 
advisable that the notes on pages 62 to 66 be 
thoroughly understood and borne in mind. 

9. Number of yards per pound. Cloths are 
sometimes made to a certain weight and the 
counts of yarns varied to make this weight; 
other cloths are made with given yarns and the 
weight figured from these. In both these 
methods item 5 is usually found in the same 
manner. 



114 PRACTICAL COTTON CALCULATIONS 

If item 5 and the weight of the cloth are 
known, the filling, item 6, may be found from 
items 4, 8 and 17 by Rule 37. See example 
after explanation of item 6. 

If item 18 is known, item 9 may be figured 
from this by Rule 68. 

Example. Item 18 gives 16.60 lbs. of yarn 
in 100 yards of cloth. 

100 yards . _ 

16.60 lbs. =6.02 yards per ft 

Item 10. Looms per set; 11. Speed of loom; 
12. Per cent, production; and 13. Weekly rate; 
are all estimated according to the width of cloth, 
quality of yarn, type of loom, and difficulty of 
pattern. 

It is while running a sample that any diffi- 
culties that are liable to be met with later in 
making an order of goods like the sample should 
be noted. The probable difficulties cannot 
always be noticed when making the sample, but 
should be when possible because the less the 
production, from any cause, the more the cost. 
If the actual production falls below that esti- 
mated, the margin between the cost and selling 
price gets smaller. 

Item 13 is mutually fixed by the head official 
and weave room overseer. 

14. Yards per week. This may be found from 
items 4, 11 and 12 by Rule 84. 

15. Weaving cost per yard. This may be 
found from items 10, 13 and 14 by Rule 92. 

Example. 145 yards X 4 looms = 580 yards 
per week from 4 looms. 



PRACTICAL COTTON CALCULATIONS 115 

.+10 weekly rate -^580 yards = 1.724c. weav- 
ing cost per yard. 

16. Con n Is and weight of warp yarns in 100 
yards of cloth. The counts of warp are obtained 
as stated in explanation of item 5. The weight 
is obtained from item 5 and length by Rule 17. 

Example. 
800 ends X 100 yards = g C)? = 3 56 

810 X 32 's counts p(mnds of 4/32 > s 

° r ' 8 !!n Dd ^ 12Qy ! rdS = 3.56 lbs. of 4/32 's 
840 X 32 's counts 

Note. The length of 100 yards is taken instead 
of 1 yard because it does not deal with so many 
small amounts, and instead of any other number 
between 1 and 100 because fewer figures are 
dealt with. When multiplying by 100, it is only 
necessary to add 2 ciphers at the right of the 
multiplicand, or to move the point 2 places to 
the right if a decimal fraction. 

17. Weight of filling in 100 yards of doth. 
This is figured out from items 4, 6 and 8 by 
Rule 34. 

Example. 

80 pick X 30 ins. X 100 yds. - ... 

OAn w nfx , —=4.76 lbs. weight 

840 X 60 s counts of fm^g. 

If item 6 is not known, item 17 may be found 
by deducting the combined weights of the warps 
from the weight of the cut, item 18. 

The loss by waste was not considered in the 
above examples when finding items 16 and 17. 



116 PRACTICAL COTTON CALCULATIONS 

The waste item is usually added in the office 
when computing the cost. 

18. Weight of cut. Say 100 yards. This 
may be found by adding items 16 and 17. 
together, or by dividing the length of cut by 
item 9, the number of yards per pound. 

Item 13 may be said to cover the weaving cost 
of cloth. To this must be added other costs 
which are necessary; these which are computed 
and arranged in the office are here numerically 
arranged as follows: 

19. Oversight per loom per week. 

20. Cost of stock. 

21. Cost of labor in making yarn. 

22. General expense per loom per week. 

Explanation of Items to be had in Office. 

19. Oversight per loom per week. These are 
probable expenses in the weave room to pay for 
overseer, fixers, all day help other than weavers, 
and supplies. This is a fixed figure, estimated 
at so much per loom, based on previous reports, 
say for six months, and verified and corrected 
from time to time. The oversight varies] in 
different mills according to the time run, and 
efficiency of the help and management ; 42c. for 
fancy, and 31c. for plain looms will be consid- 
ered here for oversight. 

20. Cost of stock. Against this is marked 
the prevailing price of raw material of the 
quality of cotton used. 



PRACTICAL COTTON CALCULATIONS 117 

21. Cost of labor in making yarns. This is 
computed from production sheets, pay rolls and 
reports of the overseers of the various depart- 
ments from the picker to the spinning room, and 
is. stated at so much per pound. 

Items 20 and 21 may be shown together on a 
blank in the office, along with the counts of the 
yarns, as follows: 





BLANK NO. 2. 






Cost of Yarns per Pound. 






Stock 






('or NTS. 


Quality. 


Pi: ice. Labor. 


Total. 


4/32 


A. 1J ins. 


12c. 4.7c. 


16.7c. 


2/32 


A. 1| ins. 


12c. 4.9c. 


16.9c. 


50 's 


B. ljins. 


14c. 6.2c. 


20.2c. 


60 's 


B. ljins. 


14c. 7.35c. 


21.35c 



The above blank only shows the items neces- 
sary for the cloth given here as an example. In 
the mill it would contain all the counts of yarn 
that they were making. 

Blank No. 2 takes in cost of spooling, slashing 
and warping, and represents the cost of the yarn 
delivered in the weave room. 

22. General expense. This is an approxi- 
mate future expense estimated at a certain 
amount per loom per week, and is intended to 
cover all general expenses, beyond those already 
indicated, incurred before the cloth reaches the 
buyer. It includes costs for taxes, insurance, 
interest, salaries, supplies, sundries, engineers, 
yard help, watchmen, lighting, oil, power, office 
expenses, cloth room, etc., and varies in most 



118 PRACTICAL COTTON CALCULATIONS 

mills. The general expense will here be as- 
sumed to be $1.80 per loom per week. 

With the data shown on blanks 1 and 2, and 
the price per week per loom for oversight and 
general expense known, the following method 
is adopted to arrive at the cost per yard and per 
pound of cloth. 

Rule 98 is first applied to find cost of yarns 
per cut, from items 16, 20 and 21. 

Example. 

3.56 lbs. 4/32 at 16.7c. = .59452 

2.56 lbs. 2/32 at 16.9c. = .43264 

5.72 lbs. 50's at 20.2c. =1.15544 

4.76 lbs. 60's at 21.35c. = 1.01626 



16.60 lbs. total weight $3.19886 total cost 
per 100 yds. of yarns per 100 

yds. of cloth 
This would be considered as $3.20. 

Rule 99 is next applied to find cost of yarns 
per yard of cloth. 

Example. 

$3.20 cost per cut . AO _ , . 

— — — ^— - = $.032 or 3.2c. cost of yarns 

100 ^ ds - per yard of cloth. 

Rule 94 is next applied to find cost per yard 
for oversight. 

Example. 

42c. oversight per loom per week ODn „ 

— = = .2896c. over- 

145 yards per loom per week { M d 



PRACTICAL COTTON CALCULATIONS 119 

Rule 95 is next applied to find cost . per yard 
for general expense. 

Example. 
$1.80 genl. expense per loom per week 



= 1.24c. 



145 yards per loom per week g-eneral 

expense per yd. 

Although the cost per yard for oversight and 
general expense may be found in one problem 
by adding the amount per week for each to- 
gether and dividing by the number of yards per 
week, the above method is usually adopted so 
that either one may be referred to again if re- 
quired. 

It is now only necessary to add the various 
costs per yard together. 

Summary of Costs per Yard of Cloth. 



Weaving, 


1.724c. 


Yarns, 


3.2 


Oversight, 


.2896 


General expense, 


1.24 



6.4536c. cost per yard. 

The cost per pound of cloth may now be 
found by multiplying the cost per yard by the 
number of yards per pound. 

Example. 6.4536c. cost per yard X 6.02 
yards per pound = 38.85c. cost per pound of 
cloth. 



120 PRACTICAL COTTON CALCULATIONS 

In a cloth mill where the yarn is bought on 
warp beams and cops or bobbins, the counts and 
price per pound would be required instead of 
blank No. 2. 

If the yarn is bought in cone or skein form, 
the costs entailed during the various processes 
necessary before it reaches the loom must be 
considered. 

There is no extra cost entailed on filling yarn 
from the time it leaves the spinningpframe or 
mule to the time that it reaches the weaver, 
beyond the cost of handling it. 

Yarn intended for warp must undergo several 
processes before it can be made into cloth, the 
principal of which are spooling, twisting, if for 
ply yarns, warping, slashing and drawing-in. 











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ct 








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© 










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o 




*>■»* 


V) 




z 




v3 


^ 
Q 




Ho 


CO 




^ 


^ 




•*o 
4^ 


•*o 
CO 


£> 


CO 

o 

pa 




cia 


ha 
c 

•»o 
CO 




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I 121 ) 



INDEX 



RULE 
NUMBER PAGE 

Average counts of cloth ... 53 

Average counts of filling in cloth contain- 
ing 2 or more counts of filling - 41 50 
Average counts of yarn in a set of warps 

containing different counts of yarn 20 36 

Average counts of yarn in cloth, from ends 

in warp, pick, width in reed and yards 

per pound - - - - 42 51 

Average counts of yarn in cloth from sley, 

pick, width and yards per pound - 43, 44 52 

Average counts of yarn in cloth from sley, 

pick, counts of warp and filling - 45 53 

Average counts of yarn in cloth with only 

one counts of warp in a cramped 

stripe - 54 

Average counts of yarn in cloth containing 

more than one counts of warp - 46, 47 54 

Average counts of yarn in cloth from per 

cent, warp, percent, filling, and counts 

of warp and filling - - - 48 56 

Average counts of yarn from a small piece 

of cloth - - - - - 49, 50 57 

Average pick when check pegs are used 53, 54 59 

Average sley from ends in warp and width 

of cloth ----- 51 58 

Average sley in an unequally reeded stripe, 

from sley and warp layout • - - 52 58 

Beam yarn and warp calculations - - 31 

Beam, counts of yarn on a, from length, 

weight and number of ends 
Beam, weight of yarn on a . 
Beam, ends on a, from counts, weight and 

length ----- 

Breaking weights of American yarns 



6 


31 


7 


32 


9 


35 




95 



123 



Cable yarns - - - - 

Change gear to give a certain number of 

picks per inch - 
Check peg patterns, calculations for 
Check pegs to use per pattern 
Cloth analysis - 

Cloth calculations - 
Cloth contraction - 
Cloth, yards per pound of - 
Cloth, ounces per yard of - 
Cloth production - 
Contraction, percentage of, in length from 

warp to cloth - 
Constants or constant numbers 
Constant to use for loom take-up motion 
Cost calculations 

Cost of filling in a piece of cloth - 
Cost of a piece of cloth 
Cost of oversight per yard - 
Cost of stock per pound of cloth - 
Cost of weaving per yard - 
Cost of yarns per cut 

Cost of yarns per pound ... 
Cost of yarns per yard of cloth 
Cost of yarn in a warp 
Costs per yard of cloth, summary of 
Cotton yarn, table of counts and lengths 

of 
Counts of cloth, average 
Counts, length or weight of cotton yarn 

(formula "A") 
Counts, number of hanks or weight 

(formula "B") 
Counts, weight, length or ends on a beam 

(formula "C") 



RULE 
NUMBER PAGE 

24 



86,87 
56, 57 



)-71 

72 



58 

85 

101 

94 
97 
92 
98 

99 
100 



101 

60 
61 
71 
51 
62 
77 
78 
99 

64 
8 
101 
105 
109 
109 
106 
107 
105 
107 
117 
108 
108 
119 

33 

58 

30 
31 
35 



RULE 




UMB 


ER 


3 AGE 






12 






13 


10 


14, 


29 


3 




14 


14 




30 

20 
20 



124 



Counts, comparing yarns for 
Counts, weighing short lengths of yarn for 
Counts, from length and weight - -1, 

Counts, from number of leas and weight 
Counts, from weight and number of hanks 
Counts, systems of numbering yarns of 

various materials for ... 
Counts, equivalent - 
Counts, equivalent, of cotton to a given 

counts of other materials - 21 

Counts, equivalent, of raw silk (yards per 

ounce system), spun silk, worsted, 

woolen and linen to a given cotton 

counts ----- 4 20 

Counts, equivalent of raw silk (denier and 

dram systems) to a given cotton 

counts ----- 23 

Counts of twisted, or ply and cable yarns 24 

Counts of single yarns equal to a ply yarn 

composed of 2 or more single yarns of 

unequal counts - - - - 5, 6 25 

Counts of yarn to twist with a given yarn 

to produce a required ply yarn 
Counts of spun silk ply yarns 
Counts of yarn on a beam from length, 

weight and number of ends 
Counts of yarn in a set of warps - 
Counts of yarn, from the weight of a few 

inches ----- 29 41 

Counts of warp or filling required to give 

a certain number of yards per pound 37 46 

Counts of filling required, from sley, pick, 

warp and average counts - - 38 48 

Counts of filling required, from sley, pick, 

width, warp and yards per pound - 39 49 

Counts of filling required in a cloth con- 
taining 2 different counts of filling 

yarn ----- 



7 


26 




28 


16 


31 


20 


36 



40 49 



INDEX. 



125 



Denier system of counts in raw silk com- 
pared to dram silk and IT. S. cotton 
counts systems - 

Dents per inch in reed to produce a given 
sley - 

Dents per inch in reed, table of 

Dents, number of, occupied by an equally 
reeded warp - 

Diameter of driving pulley 

Diameter of loom pulley 

Diameters of yarns - 

Dram system of counts in raw silk com- 
pared to denier silk and U. S. cotton 
counts systems 

Ends on a beam, from counts, weight and 
length ----- 

Ends, number of, in an equally reeded 
warp ----- 

Ends* number of, in an unequally reeded 

pattern, from sley, width and warp 

layout ----- 

Equivalent counts - - - - 

Equivalent counts in various systems, 

short methods to find - 
Expense per yard of cloth, general 
Expense per pound of cloth, general 

Filling calculations, warp and 
Filling calculations - 

Filling, weight of, per cut from per cent, 
of filling . . . . 

Filling, required per day, weight of 

Filling, hanks of, in a piece of cloth 

Filling, per cut, weight of - 

Filling, counts of, required to give a cer- 
tain number of yards per pound 

Filling, counts of, required from sley, pick, 
warp counts and average counts 



RULE 
NUMBER PAGE 



23 



60 


67 




68 


64 


71 


89 


103 


90 


103 


80,81 


92 



23 



19 


35 


21 


36 


25 


38 




20 




20 


95 


106 


96 


106 




41 




43 


30 


41 


31 


42 


32 


43 


34 


44 


37 


46 


38 


48 



126 INDEX. 



RULE 
NUMBER PAGE 



Filling, counts of, required from sley, 
pick, width, warp counts and yards 
per pound - - - * - 39 49 

Filling, counts of, required in a cloth con- 
taining two different counts of rilling 
yarn ----- 40 49 

Filling, average counts of, in a piece of 

cloth containing 2 or more counts of 

filling ----- 41 50 

Filling, percentage of 73—77 82 

Filling, cost of, in a piece of cloth - 101 109 

Gear, change, to use to give a certain 

number of picks per inch - - 86, 87 101 

Glossary of technical words and terms - 5 

Ground picks per inch, from average pick, 

number of teeth used per pattern and 

picks per pattern - - - 55 60 

Hank of roving, number of 
Hanks, from weight and counts - 
Hanks of warp yarn in a piece of cloth 
Hanks in a warp, from ends and length ■ 
Hanks of rilling, from pick, width in reed 

and length - - - - 32 43 

Hanks of yarn, warp or rilling, in 100 

yards of cloth, table of - - 80 

Length for cotton, standard of - - 11 

Length and weight standards - - 11 
Length, weight or counts of cotton yarn 

(formula "A") - - - 30 
Length, weight, counts or number of ends 

on a beam (formula "C") - - 35 

Length and counts table - 33 

Length, from counts and weight - - 11 29 
Length of yarn on a beam, from weight, 

counts and number of ends - - 18 34 





* 14 


15 


31 


22 


37 


23 


37 



INDEX. 127 



RULE 
NUMBER PAGE 



Length of yarn on a warp, from number 

of hanks and number of ends 24 38 

Length of cloth that can be woven with a 

given counts and weight of filling - 33 43 

Length of warp required for a given length 

of cloth in lenos, lappetts, etc. - 59 65 

Loom calculations - 101 

Metric system compared to U. S. cotton 

counts system - 20 

Numbering cotton yarn, standard for - 16 

Numbering yarns of various materials, 

systems of 20 

Ounces per yard, from yards per pound - 65 74 
Ounces per yard, from a small piece of 

cloth - - - 72 79 

Oversight per yard, cost of - - 94 106 

Patterns, number of, in an unequally 

reeded cloth - 26 39 

Percentage of contraction in length from 

warp to cloth - 58 64 

Percentage of warp or tilling in any cloth 73 82 

Percentage of warp or filling in cloth, 

from ends, pick, warp, rilling and 

width ----- 74 84 

Percentage of warp or filling in cloth, 

from sley, pick, warp and filling 

counts ----- 76 85 

Percentage of warp or rilling in cloth, 

from weight of warp and weight of 

cut - - - 75 85 

Percentage of warp or filling in cloth, 

from sley, pick, average counts and 

warp - - - - 77 86 

Per cent, of production of a loom - - 82-84 99 

Pick, average, when check pegs are used - 53, 54 59 



128 



Picks per inch, ground, from average pick, 
number of teeth used and picks per 
pattern ----- 

Ply and cable yarns, counts of twisted or, 
Ply yarns, counts of, composed of 2 or 

more single yarns of unequal counts 
Ply yarn, counts of a yarn to twist with a 

given yarn to produce a required 
Ply yarns, counts of spun silk 
Production tables, cloth ... 
Production of cloth per week 

Raw silk calculations 

Raw silk counts compared to cotton 
counts ----- 

Reed calculations - 

Reed to use for unequally reeded patterns 

Reed, width in, from sley and width of 

cloth ----- 

Reed, dents per inch in, for a given sley - 
Reed table ----- 
Reeling yarns 

Size, per cent, of, on warp yarns - - 27 40 

Sley that would be woven with a reed of 

a given number of dents per inch - 61 69 

Sley. average, from ends and width of 

cloth ----- 51 58 
Sley, average, in an unequally reeded 

stripe from sley and warp layout - 52 58 

Speed calculations - 102 

Speed of shafting - - - 88 102 

Speed of loom - - - - 91 104 

Spun silk ply yarns, counts of - - 28 

Square root of numbers 1 to 140 - - 90, 91 

Square yards in a cut of cloth - - 78, 79 87 



RULE 




NUMBER PAGE 


55 


60 




24 


5,6 


25 


7 


26 




28 


97 


98 


82 


99 




22 




23 




65 


62 


69 


63 


70 


60 


67 




73 




14 



INDEX. 129 

RULE 
NUMBER PAGE 

Standards of lengths and weights for 

textile materials ... 11 

Systems of filling out blank with weave 

room data for a piece of cloth - 111 

Tables for counting cotton yarn, from 

weight in grains of 120 yards - - 16-20 

Tables of cloth production - 97, 98 
Table of dents per inch in reed to produce 

any even numbered sley from 48 to 132 68 
Table of dents per fa inch (1 to 20) to 

weave cloths with from 48 to 112 sley 

ground ----- 73 

Table of lengths and counts - - 8 

Table of length and weight : - 8 
Tables of hanks of yarn, warp or filling, in 

100 yards of cloth - 80, 81 
Table of yards of yarn per pound in counts 

from 1 to 250 - - - - 33 

Take-up in length from warp to cloth - 58 64 

Technical words and terms, glossary of - 5 

Testing yarns for counts by comparison - 12 

Testing yarns for strength - 93 

Twisted or ply and cable yarns, counts of 24 

Twists per inch in yarns ... 88 

Twist tables - - 90, 91 

Warp calculations, beam yarn and - 31 

Warp, length of, from number of hanks 

and number of ends - - - 24 38 

Warp and filling calculations - - 41 

Warp required per day, weight of - 31 42 

Warp, counts of, from sley, pick, filling 

and average counts - - - 38 48 

Warp, length of, required for a given 

length of cloth in lenos, lappetts, etc. 
Warp, percentage of 
Weaving, cost of - 



73-77 


82 


92, 1)3 


105 



9 


27 


12 


29 


13 


30 




30 




31 




35 


28 


'40 



130 INDEX. 

RULE 
NUMBER PAGE 

Weight and length standards - - 11 

Weight required of each count for a given 

weight of ply yarn 8 26 

Weight required of each counts in a group 

of warps, from counts, number of 

ends of each and total weight - 
Weight, from counts and length - 
Weight, from counts and number of hanks 
Weight, counts or length of cotton yarn 

(formula "A") 
Weight, counts or number of hanks of 

yarn (formula "B") - 
Weight, length, counts or number of ends 

on a beam (formula "C") 
Weight of warp in ounces per yard of cloth 
Weight of warp per cut from per cent. 

warp ----- 30 41 

Weight or number of yards per pound and 

ounces per yard - 74 

Weight of yarn on a beam, from length, 

number of ends and counts - - 17 32 

Weight of warp yarn on beams in the 

looms ----- 34 

Weight of warp yarn in a piece of cloth - 17 32 

Weight of each separate color of filling 

required for colored check fabrics - 35 44 

Weight of each count or kind of filling 

required for embossed fabrics - - 36 45 

Weight of filling required for stop peg 

checks ----- 44 

Weight of fillin j required per cut - - 34 44 

Weight or yards per pound - - 74 

Width in reed, from sley and width of 

cloth ----- 03 70 

Yards per pound of a cloth containing 
different counts of yarns or patterns 
that are unequally reeded - - 67, 68 75 



131 



Yards of cloth per pound, from ounces 

per yard 
Yards of cloth per pound, from sley, pick, 

width and average counts 
Yards of cloth per pound, from sley, pick, 

width, warp and filling counts 
Yards of cloth per pound from a small 

piece of cloth - 
Yarn, counts of, from any number of 

yards reeled or measured 
Yarn calculations - 
Yarn standard - - - 

Yarn, weight of, from counts and hanks 
Yarn, counts, length or weight of 

(formula "A") 
Yarn, length of, from counts and weight 
Yarn, weight of, from counts and length 
Yarn, counts of, from length and weight 
Yarn, counts of, from weight and hanks 
Yarn and warp calculations, beam 
Yarn on a beam, counts of 
Yarn on a beam, weight of 
Yarn on a beam, length of 
Yarn, counts of, from weight of a few 

inches - 
Yarns, cost of, per yard and per cut 
Yarns, cost of, in a warp - 
Yarns, diameters of - 

Yarns, reeling - 

Yarns, testing, for strength 
Yarns, testing, for counts by comparison 
Yarns, testing, for counts by weighing 

short lengths ... 
Yarns, twists per inch in - 
Yarns of various materials, systems of 

numbering - 



rule 

NUMBER 

65 
69 

'0, 71 
66 
1,2. 

13" 



11 
12 
10 
14 

16 
17 

18 

29 

- 98, 99 

- 100 



PAGE 

74 
77 



14 
11 
11 
30 

30 
29 
29 
29 
30 
31 
31 
32 
34 

41 
107 
108 
92 
14 
93 
12 

13 
88 

20 



Howard & Bullough 


American Machine Company, Ltd. 


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NEWTON UPPER FALLS, MASS. 



Southern Agent 
A. H. WASHBURN, CHARLOTTE, N. C. 

{ L33 I 




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Jacquard Card Machinery 







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( 135 i 



IJYY/E manufacture improved cotton 
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DRAPER COMPANY 




FRANK C. LITCHFIELD, Pres. GEO. M. CHENEY, Treas. 

H. L. LITCHFIELD, Clerk 



Established 1843 



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STUART W. CRAMER, Southern Agent 
Trust Building, CHARLOTTE, N. C. 
Equitable Building, ATLANTA, GA. 

( 138 ) 






American 
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HAY 24 190T 



